Statement-1: If \( f(x)=\frac{2}{\pi} \cot ^{-1}\left(\frac{3 x^{2}+1}{(x-1)(x-2)}\right) \), th....

Channel:
PW Solutions
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=Gtalub_WWd0


Duration: 2:20
0 views
0

Statement-1: If \( f(x)=\frac{2}{\pi} \cot ^{-1}\left(\frac{3 x^{2}+1}{(x-1)(x-2)}\right) \),
\( \mathrm{P} \)
then \( \lim _{x \rightarrow 1^{-}} f(x)=0 \) and \( \lim _{x \rightarrow 2^{-}} f(x)=2 \)
Statement-2: \( \lim _{x \rightarrow \infty} \cot ^{-1} x=0 \) and
\[
\lim _{x \rightarrow-\infty} \cot ^{-1} x=\pi
\]
(A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1.
(C) Statement-1 is True, Statement-2 is False.
(D) Statement-1 is False, Statement-2 is True.


πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2024-01-21Let \( f(x)=\lim _{n \rightarrow \infty}(\sin x)^{2 n} \), then \( f \) is:....
2024-01-21Let \( f(x)=\left|\begin{array}{ccc}x^{3} & 2 x^{2} & -x \\ 2 x & 1 & 0 \\ x & 0 & 3\end{array}\....
2024-01-21If \( x=e^{t} \cos t \) and \( y=e^{t} \sin t \) then the value of \( \frac{d y}{d x} \) at \( t....
2024-01-21If \( y=\tan ^{-1}\left(\frac{x}{2}\right)+\sin ^{-1}\left(\frac{2}{\sqrt{4+x^{2}}}\right) \) th....
2024-01-21If \( f(x)=\left\{\begin{array}{cc}x^{2}\left(\frac{e^{1 / x}-e^{-1 / x}}{e^{1 / x}+e^{-1 / x}}\....
2024-01-21If \( y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots .+\frac{x^{n}}{n !}+\ldots . . \infty \) ....
2024-01-21If \( 3 x^{2}-10 x y+5 y^{2}=0 \) then \( \frac{d y}{d x} \) is equal to :....
2024-01-21Derivative of ' \( y \) ' if \( y=\frac{1}{\sec x-\tan x} \)....
2024-01-21If \( y=x^{x^{2}} \), find \( \frac{d y}{d x} \)....
2024-01-21The derivative of ' \( \sec ^{2} x \) ' with respect to ' \( \tan x \) ' is....
2024-01-21Statement-1: If \( f(x)=\frac{2}{\pi} \cot ^{-1}\left(\frac{3 x^{2}+1}{(x-1)(x-2)}\right) \), th....
2024-01-21The number of points of non differentiability of the function \( f(x)=|\sin x|+\sin |x| \) in \(....
2024-01-21Statement-1: \( \lim _{x \rightarrow \infty}\left(\frac{1}{x^{2}}+\frac{2}{x^{2}}+\frac{3}{x^{2}....
2024-01-21If \( \lim _{n \rightarrow \infty} \frac{n^{98}}{n^{x}-(n-1)^{x}}=\frac{1}{99} \), then the valu....
2024-01-21If \( f(x)=x \sin \left(\frac{\pi}{2}(x+2[x])\right) \), then \( f(x) \) is \( \{ \) where [.] d....
2024-01-21Let \( f^{\prime \prime}(x) \) be continuous at \( x=0 \) and \( f^{\prime \prime}(0)=4 \) then ....
2024-01-21The function \( f(x)=\sin ^{-1}(\cos x) \) is:....
2024-01-21Statement-1: \( \lim _{x \rightarrow 0}\left[\frac{\sin x}{x}\right]=0 \) Statement - 2: \( \lim....
2024-01-21Consider \( f(x)=\frac{\sin x+a e^{x}+b e^{-x}+c \ln (1+x)}{x^{3}} \), where \( a, b, c \) are r....
2024-01-21Let \( f(x)=\left\{\begin{array}{cc}x \sin \left(\frac{1}{x}\right)+\sin \left(\frac{1}{x^{2}}\r....
2024-01-21The value of \( \lim _{x \rightarrow 0} x^{2}\left[\frac{1}{x^{2}}\right] \) is (where [.] denot....