જો f(0) = 2 હોય,તો mathop {lim }limits_{x to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) ધારો કે $L = \mathop {\lim }\limits_{x 	o 0} \frac{{\int\limits_0^x {tf(x)dt + \int\limits_0^x xf(t)dt} }}{{{x^2}}}$$L = \mathop {\lim }\limits_{

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) ધારો કે $L = \mathop {\lim }\limits_{x 	o 0} \frac{{\int\limits_0^x {tf(x)dt + \int\limits_0^x xf(t)dt} }}{{{x^2}}}$$L = \mathop {\lim }\limits_{x 	o 0} \frac{{f(x) \int\limits_0^x t dt + x \int\limits_0^x f(t) dt}}{{{x^2}}}$$L = \mathop {\lim }\limits_{x 	o 0} \frac{{f(x) \cdot \frac{x^2}{2} + x \int\limits_0^x f(t) dt}}{{{x^2}}}$$L = \mathop {\lim }\limits_{x 	o 0} \left( \frac{f(x)}{2} + \frac{\int\limits_0^x f(t) dt}{x} ight)$બીજા પદ માટે $L$'Hopital ના નિયમનો ઉપયોગ કરતા: $\mathop {\lim }\limits_{x 	o 0} \frac{\int\limits_0^x f(t) dt}{x} = \mathop {\lim }\limits_{x 	o 0} \frac{f(x)}{1} = f(0)$$L = \frac{f(0)}{2} + f(0) = \frac{3}{2} f(0)$$f(0) = 2$ આપેલ હોવાથી,$L = \frac{3}{2} 	imes 2 = 3$.

જો $f(0) = 2$ હોય,તો $\mathop {\lim }\limits_{x \to 0} \frac{{\int\limits_0^x {\left( {tf(x) + xf(t)} \right)dt} }}{{{x^2}}}$ ની કિંમત શોધો.

Similar Questions

$\mathop {\lim }\limits_{x \to \infty } \frac{{{x^n}}}{{{e^x}}} = 0$ માટે

જો $\lim _{x \rightarrow 0} \frac{a x e^{x}-b \log (1+x)}{x^{2}}=3$ હોય,તો $a$ અને $b$ ની કિંમતો અનુક્રમે શું થાય?

$\lim _{x \rightarrow 0} \frac{x 2^{x}-x}{1-\cos x}$ ની કિંમત શોધો.

$\lim _{x \rightarrow 3^{-}} \frac{x^3-3 x^2-4 x+12}{2 x^3-7 x^2+2 x+3} = $

$\mathop {\lim }\limits_{x \to 0} \left[ {\frac{{{e^x} - {e^{\sin x}}}}{{x - \sin x}}} \right]$ ની કિંમત શોધો.

Vedclass Test Series

Exam Paper Generator

Online Exam Module