mathop {lim }limits_{x to 0} frac{{{{tan }^{ | vedclass

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

Question

(D) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{{{	an }^{ - 1}}x}}{x}$.Substituting $x = 0$,we get the indeterminate form $\frac

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{{{	an }^{ - 1}}x}}{x}$.Substituting $x = 0$,we get the indeterminate form $\frac{0}{0}$.Using $L$'$H$ôpital's rule,we differentiate the numerator and the denominator with respect to $x$:$\frac{d}{dx}(	an^{-1}x) = \frac{1}{1+x^2}$ and $\frac{d}{dx}(x) = 1$.Thus,$\mathop {\lim }\limits_{x 	o 0} \frac{\frac{1}{1+x^2}}{1} = \mathop {\lim }\limits_{x 	o 0} \frac{1}{1+x^2}$.Evaluating the limit as $x 	o 0$,we get $\frac{1}{1+0^2} = 1$.

$\mathop {\lim }\limits_{x \to 0} \frac{{{{\tan }^{ - 1}}x}}{x}$ is

Similar Questions

$\mathop {Limit}\limits_{x \to 0} {(\cos 2x)^{3/x^2}}$ has the value equal to . . . . . . .

The value of $\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\int_{\frac{\pi }{2}}^x t \,dt}}{{\sin (2x - \pi )}}$ is

Evaluate the limit: $\lim _{x \rightarrow 2} \frac{x^3-x^2-x-2}{2 x^3-3 x^2-3 x+2}$

Evaluate the limit: $\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$

If $f^{\prime \prime}(0)=k, k \neq 0,$ then the value of $\lim _{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^{2}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module