{"id":542008,"date":"2021-09-27T09:35:30","date_gmt":"2021-09-27T09:35:30","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=542008"},"modified":"2022-12-26T09:35:22","modified_gmt":"2022-12-26T09:35:22","slug":"rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/","title":{"rendered":"RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations"},"content":{"rendered":"\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">Class 12: Maths Chapter 14 solutions. Complete Class 12 Maths Chapter 14 Notes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\">RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations<\/h2>\n\n\n\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">RD Sharma 12th Maths Chapter 14, Class 12 Maths Chapter 14 solutions<\/p>\n\n\n\n<p>Exercise 14.1 Page No: 14.9<\/p>\n\n\n\n<p><strong>1. If y = sin x and x changes from \u03c0\/2 to 22\/14, what is the approximate change in y?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"639\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-1.png\" alt=\"\" class=\"wp-image-542013\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-1.png 595w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-1-279x300.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-1-400x430.png 400w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"234\" height=\"52\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-2.png\" alt=\"\" class=\"wp-image-542014\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"340\" height=\"126\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-3.png\" alt=\"\" class=\"wp-image-542018\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-3.png 340w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-3-300x111.png 300w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/figure>\n\n\n\n<p><strong>2. The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given the radius of a sphere changes from 10 cm to 9.8 cm.<\/p>\n\n\n\n<p>Let x be the radius of the sphere and \u0394 x be the change in the value of x.<\/p>\n\n\n\n<p>Hence, we have x = 10 and x + \u0394 x = 9.8<\/p>\n\n\n\n<p>\u21d2&nbsp;10 + \u0394 x = 9.8<\/p>\n\n\n\n<p>\u21d2&nbsp;\u0394 x = 9.8&nbsp;\u2013 10<\/p>\n\n\n\n<p>\u2234&nbsp;\u0394 x =&nbsp;\u2013 0.2<\/p>\n\n\n\n<p>The volume of a sphere of radius x is given by<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"650\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-4.png\" alt=\"\" class=\"wp-image-542019\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-4.png 594w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-4-274x300.png 274w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-4-400x438.png 400w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"592\" height=\"387\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-5.png\" alt=\"\" class=\"wp-image-542020\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-5.png 592w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-5-300x196.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-5-400x261.png 400w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/figure>\n\n\n\n<p><strong>3. A circular metal plate expands under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"310\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-6.png\" alt=\"\" class=\"wp-image-542021\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-6.png 601w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-6-300x155.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-6-400x206.png 400w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"597\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7.png\" alt=\"\" class=\"wp-image-542022\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7.png 595w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7-300x300.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7-400x401.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-7-200x200.png 200w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure>\n\n\n\n<p><strong>4. Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"641\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-9.png\" alt=\"\" class=\"wp-image-542023\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-9.png 606w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-9-284x300.png 284w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-9-400x423.png 400w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"192\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-10.png\" alt=\"\" class=\"wp-image-542024\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-10.png 538w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-10-300x107.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-10-400x143.png 400w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/figure>\n\n\n\n<p><strong>5. If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"603\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-11.png\" alt=\"\" class=\"wp-image-542025\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-11.png 626w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-11-300x289.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-11-400x385.png 400w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"105\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-12.png\" alt=\"\" class=\"wp-image-542026\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"300\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-13.png\" alt=\"\" class=\"wp-image-542027\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-13.png 479w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-13-300x188.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-13-400x251.png 400w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/figure>\n\n\n\n<p><strong>6. The pressure p and the volume v of a gas are connected by the relation pv<sup>1.4<\/sup>&nbsp;= const. Find the percentage error in p corresponding to a decrease of \u00bd %&nbsp;in v.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"514\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-14.png\" alt=\"\" class=\"wp-image-542028\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-14.png 469w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-14-274x300.png 274w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-14-400x438.png 400w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"486\" height=\"196\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-16.png\" alt=\"\" class=\"wp-image-542029\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-16.png 486w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-16-300x121.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-16-400x161.png 400w\" sizes=\"auto, (max-width: 486px) 100vw, 486px\" \/><\/figure>\n\n\n\n<p><strong>7. The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase in (i) in total surface area, and (ii) in the volume, assuming that k is small.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"615\" height=\"198\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-17.png\" alt=\"\" class=\"wp-image-542030\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-17.png 615w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-17-300x97.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-17-400x129.png 400w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"359\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-18.png\" alt=\"\" class=\"wp-image-542031\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-18.png 298w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-18-249x300.png 249w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"454\" height=\"401\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-19.png\" alt=\"\" class=\"wp-image-542032\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-19.png 454w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-19-300x265.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-19-400x353.png 400w\" sizes=\"auto, (max-width: 454px) 100vw, 454px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"637\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-20.png\" alt=\"\" class=\"wp-image-542033\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-20.png 555w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-20-261x300.png 261w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-20-400x459.png 400w\" sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"297\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-21.png\" alt=\"\" class=\"wp-image-542034\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-21.png 589w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-21-300x151.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-21-400x202.png 400w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"576\" height=\"628\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-22.png\" alt=\"\" class=\"wp-image-542035\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-22.png 576w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-22-275x300.png 275w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-22-400x436.png 400w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"274\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-23.png\" alt=\"\" class=\"wp-image-542036\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-23.png 587w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-23-300x140.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-23-400x187.png 400w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"571\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-24.png\" alt=\"\" class=\"wp-image-542037\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-24.png 598w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-24-300x286.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-24-400x382.png 400w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/figure>\n\n\n\n<p><strong>8. Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"540\" height=\"190\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-25.png\" alt=\"\" class=\"wp-image-542038\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-25.png 540w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-25-300x106.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-25-400x141.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"592\" height=\"636\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-26.png\" alt=\"\" class=\"wp-image-542039\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-26.png 592w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-26-279x300.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-26-400x430.png 400w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"267\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-27.png\" alt=\"\" class=\"wp-image-542040\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"60\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations-image-28.png\" alt=\"\" class=\"wp-image-542041\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 14 Differentials, Errors and Approximations\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-12-maths-chapter-14-download-pdf\">RD Sharma Solutions for Class 12 Maths Chapter 14:&nbsp;<strong>Download PDF<\/strong><\/h2>\n\n\n\n<p>RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations<\/p>\n\n\n\n<p><a href=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solutions-for-Class-12-Maths-Chapter-14\u2013Differentials-Errors-and-Approximations.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download PDF<\/strong>: RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations PDF<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-chapterwise-rd-sharma-solutions-for-class-12-maths\"><strong>Chapterwise RD Sharma Solutions for Class 12&nbsp;Maths :<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-1-relation\/\">Chapter 1\u2013Relation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-2-functions\/\">Chapter 2\u2013Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-3-binary-operations\/\">Chapter 3\u2013Binary Operations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-4-inverse-trigonometric-functions\/\">Chapter 4\u2013Inverse Trigonometric Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-5-algebra-of-matrices\/\">Chapter 5\u2013Algebra of Matrices<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-6-determinants\/\">Chapter 6\u2013Determinants<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-7-adjoint-and-inverse-of-a-matrix\/\">Chapter 7\u2013Adjoint and Inverse of a Matrix<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-8-solution-of-simultaneous-linear-equations\/\">Chapter 8\u2013Solution of Simultaneous Linear Equations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-9-continuity\/\">Chapter 9\u2013Continuity<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-10-differentiability\/\">Chapter 10\u2013Differentiability<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-11-differentiation\/\">Chapter 11\u2013Differentiation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-12-higher-order-derivatives\/\">Chapter 12\u2013Higher Order Derivatives<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-13-derivatives-as-a-rate-measurer\/\">Chapter 13\u2013Derivatives as a Rate Measurer<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\">Chapter 14\u2013Differentials, Errors and Approximations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-15-mean-value-theorems\/\">Chapter 15\u2013Mean Value Theorems<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-16-tangents-and-normals\/\">Chapter 16\u2013Tangents and Normals<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-17-increasing-and-decreasing-functions\/\">Chapter 17\u2013Increasing and Decreasing Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-18-maxima-and-minima\/\">Chapter 18\u2013Maxima and Minima<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\">Chapter 19\u2013Indefinite Integrals<\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">About RD Sharma<\/h2>\n\n\n\n<p>RD Sharma i<em>sn&#8217;t the kind of author you&#8217;d bump into at lit fests. But his bestselling books have helped many&nbsp;<\/em>CBSE<em>&nbsp;students lose their dread of&nbsp;<\/em>maths<em>. Sunday Times profiles the tutor turned internet star<\/em><br>He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like &#8216;series solution of linear differential equations&#8217;. Meet Dr&nbsp;Ravi Dutt Sharma&nbsp;\u2014&nbsp;mathematics&nbsp;teacher and author of 25 reference books \u2014 whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it&#8217;s only recently that a spoof video turned the tutor into a YouTube star.<\/p>\n\n\n\n<p>R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. &#8220;I like to spend all my time thinking and writing about maths problems. I find it relaxing,&#8221; he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government&#8217;s Guru Nanak Dev Institute of Technology.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">RD Sharma Solutions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/ncert-class-xii\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">NCERT Class 12 Solutions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-class-12\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">RD Sharma Class 12 <strong>Solutions<\/strong><\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Class 12: Maths Chapter 14 solutions. Complete Class 12 Maths Chapter 14 Notes. RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations RD Sharma 12th Maths Chapter 14, Class 12 Maths Chapter 14 solutions Exercise 14.1 Page No: 14.9 1. If y = sin x and x changes from \u03c0\/2 to 22\/14, [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":542011,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,25],"tags":[1961],"boards":[],"class_list":["post-542008","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-12","tag-rd-sharma-solutions-vol-1","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>RD Sharma Solutions for Class 12, maths Chapter 14 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations | Browse Class 12 Maths Ch - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations\" \/>\n<meta property=\"og:description\" content=\"Class 12: Maths Chapter 14 solutions. Complete Class 12 Maths Chapter 14 Notes. RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-27T09:35:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-12-26T09:35:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/class12-m14.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"675\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"RD Sharma Solutions for Class 12 Maths Chapter 14\u2013Differentials, Errors and Approximations\",\"datePublished\":\"2021-09-27T09:35:30+00:00\",\"dateModified\":\"2022-12-26T09:35:22+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\"},\"wordCount\":667,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/class12-m14.png\",\"keywords\":[\"RD Sharma Solutions Vol 1\"],\"articleSection\":[\"Book Solutions\",\"Class 12\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\",\"name\":\"RD Sharma Solutions for Class 12, maths Chapter 14 - 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