If \( f(x)=\left\{\begin{array}{cc}\frac{\sin \{\cos x\}}{x-\frac{\pi}{2}} & x \neq \frac{\pi}{2... VIDEO
If \( f(x)=\left\{\begin{array}{cc}\frac{\sin \{\cos x\}}{x-\frac{\pi}{2}} & x \neq \frac{\pi}{2} \\ 1 & x=\frac{\pi}{2}\end{array}\right. \), where \( \{k\} \) represents the fractional part of \( k \), then:
(a) \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)
(b) \( \lim _{x \rightarrow \frac{\pi}{2}} f(x) \) dos not exist
(c) \( \lim _{x \rightarrow \frac{\pi}{2}} f(x) \) exists, but \( f \) is not continous at \( x=\frac{\pi}{2} \)
(d) \( \lim _{x \rightarrow \frac{\pi}{2}} f(x)=1 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-08 (a) An infinite discontinuity
(b) Finite discontinuity
(c) Oscillatory discontinuity
(d) A remov... 2023-06-08 If \( y=(\sin x)^{\left.(\sin x)^{(\sin x)}\right)^{\infty}} \), then \( \frac{d y}{d x}= \)
(a)... 2023-06-08 Amongst the following functions, a function that is differentiable at \( x=0 \) is
(a) \( \cos (... 2023-06-08 Let \( f(x)=|| e^{x}-1|-1| \) then \( f(x) \) is differentiable at all points except at \( x=0 \... 2023-06-08 If \( y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \), then which of the following is false?
(a)... 2023-06-08 The number of points of discontinuity of \( y=f(t) \), where \( f(t)=\frac{3}{2 t^{2}+5 t-3} \) ... 2023-06-08 Let \( f(x)=1+4 x-x^{2} \) and \( g(x)=\left\{\begin{array}{l}\max \{f(t), x \leq t \leq x+1\}, ... 2023-06-08 If \( f(x)=\left(\frac{x}{2}\right)-1 \), then on the interval \( [0, \pi] \)
(a) \( \tan (f(x))... 2023-06-08 Let \( f \) be a polynomial function such that \( f(3 x)=f^{\prime}(x) \cdot f^{\prime \prime}(x... 2023-06-08 If function \( f(x)=\frac{\sin x}{\sin \frac{1}{x}} \) is discontinuous at \( k \) points in \( ... 2023-06-08 If \( f(x)=\left\{\begin{array}{cc}\frac{\sin \{\cos x\}}{x-\frac{\pi}{2}} & x \neq \frac{\pi}{2... 2023-06-08 Let \( f(x)=\operatorname{sgn}(x) \) and \( h(x)=x\left(x^{2}-5 x+6\right) \). The function \( f... 2023-06-08 A point \( (x, y) \), where function \( f(x)=[\sin [x]] \) in \( (0,2 \pi) \) is not continuous ... 2023-06-08 Let \( f(x)=-1+|x-2| \) and \( g(x)=1-|x| \) then set of all possible value(s) of \( x \) for wh... 2023-06-08 Let \( \alpha \) be a positive real number. Let \( f: R \rightarrow R \) and \( g:(\alpha, \inft... 2023-06-08 \( A B C \) is an isosceles triangle inscribed in a circle of radius \( r \). If \( A B=A C \) a... 2023-06-08 If \( \beta=\lim _{x \rightarrow 0} \frac{e^{x^{3}}-\left(1-x^{3}\right)^{\frac{1}{3}}+\left(\le... 2023-06-08 If \( y=\frac{1}{p^{2}+p-2} \) where \( p=\frac{1}{x-1} \), then the number of points of discont... 2023-06-08 \( \lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}} \) is equal to
(a) 2
(... 2023-06-08 If \( \lim _{x \rightarrow 0} \frac{\alpha e^{x}+\beta e^{-x}+\gamma \sin x}{x \sin ^{2} x}=\fra... 2023-06-08 Let \( \beta=\lim _{x \rightarrow 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x...