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[mathjax] Exercise 19.3 Question 1 $\displaystyle\int(x+2) \sqrt{3 x+5} d x$ Sol : Let $z=3 x+5$ then $\dfrac{d z}{d x}=3 $ ∴$d x=\dfrac{d z}{3}$ Again z=3 x+5 ∴ $x=\dfrac{2-5}{3}$ Now,...
[mathjax] Exercise 19.2 Question 1 (i) $\displaystyle\int \dfrac{dx}{\sqrt{x+a}+\sqrt{x+b}}$ Sol : =$\displaystyle\int \dfrac{\sqrt{x+a}-\sqrt{x+b}}{(\sqrt{x+a}+\sqrt{x+b})((\sqrt{x+a}-\sqrt{x+b})}dx$...
[mathjax] Question 1 ∫(x 2 -5x+7)dx Sol : = ∫x 2 dx-5∫xdx+7∫dx [∵ ∫x n dx=$\dfrac{x^{n+1}}{n+1}$] =$\dfrac{x^3}{3}-\dfrac{5x^2}{2}+7x+c$ Question 2 ∫(ax 3 -bx 2 +cx+d)dx Sol : =a∫x 3 dx+b∫x 2...
[mathjax] Question 1 (a) निम्नलिखित फलनो के सभी स्थानीय उच्चतम और निम्नतम बिन्दुएँ , यदि कोई हो , तो ज्ञात कीजिए तथा संगत उच्चतम और निम्नतम मान निम्नतम मान जैसी हो , भी ज्ञात कीजिए । (i) f (x)=x 3...
[mathjax] Question 1 अवकल का प्रयोग करते हुए निम्नलिखित मे प्रत्येक का सन्निकट मान दशमलव के 3 स्थानो तक निकाले । [Using differentials, find the approximate value of each of the following upto 3...
[mathjax] Question 1 x=2 पर वक्र y=x 3 -x की ढाल ज्ञात करे । [Find the slope of the curve y=x 3 -x at x=2] Sol : y=x 3 -x Differentiating w.r.t x $\frac{dy}{dx}=3x^2-1$ x=2 पर ,...
[mathjax] Question 1 अन्तराल निकाले जिसमे निम्रलिखित फलन वर्धमान या हासमान हे [Find the intervals in which the following functions are increasing or decreasing] (i) $f(x)=10-6 x-2 x^{2}$ (ii) $f(x)=2...
[mathjax] Question 1 धातु के एक वर्गाकार पतर की भुजा 3cm/minute की दर से बढ रही है । किस दर से क्षेत्रफल बढ़ रहा है जब भुजा को लम्बाई 10cm है ? [The side of a square sheet of metal is increasing at...
[mathjax] Question 1 फलन f (x)=(x-2) log x पर विचार करते हुए सिद्द करे कि समीकरण xllogx=2-x और 2 के बिच मे x कम-से-कम एक मान के लिए अवश्य सत्य है । [Considering the function f (x)=(x-2)log x, show...
[mathjax] निम्नलिखित फलनों के द्वितीय(कोटि) का अवकलज ज्ञात करें । [Find the second order derivatives of the following functions] (i) log x Sol : माना y=log x Differentiating w.r.t x $\frac{d...
Ever heard the saying, "Knowledge is power"? In the realm of education, this couldn't be more accurate. Let's dive into the world of Lakhmir Singh and Manjit Kaur Solutions and discover the power of...
[mathjax] Question 1 $\frac{d y}{d x}$ ज्ञात करे जब [Find $\frac{d y}{d x}$ when] (i) x=acosθ , y=asinθ Sol : Differentiate w.r.t θ $\frac{d x}{d \theta}=-a \sin \theta$..(i) $\frac{d y}{d \theta}=a...