86
MCQ (Single Correct Answer)
The function $f(x)=\cot x$ is discontinuous on the set
A
$\{x=n \pi: n \in Z\}$
B
$\{x=2 n \pi: n \in Z\}$
C
$\left\{x=(2 n+1) \frac{\pi}{2} ; n \in Z\right\}$
D
$\left\{x=\frac{n \pi}{2} ; n \in Z\right\}$
87
MCQ (Single Correct Answer)
The function $f(x)=e^{|x|}$ is
A
continuous everywhere but not differentiable at $x=0$
B
continuous and differentiable everywhere
C
not continuous at $x=0$
D
None of the above
88
MCQ (Single Correct Answer)
If $f(x)=x^2 \sin \frac{1}{x}$, where $x \neq 0$, then the value of the function $f$ at $x=0$, so that the function is continuous at $x=0$, is
A
0
B
$-$1
C
1
D
None of these
89
MCQ (Single Correct Answer)
If $f(x)=\left[\begin{array}{ll}m x+1, & \text { if } x \leq \frac{\pi}{2} \\ \sin x+n, & \text { if } x>\frac{\pi}{2}\end{array}\right.$ is continuous at $x=\frac{\pi}{2}$, then
A
$m=1, n=0$
B
$m=\frac{n \pi}{2}+1$
C
$n=\frac{m \pi}{2}$
D
$m=n=\frac{\pi}{2}$
90
MCQ (Single Correct Answer)
If $f(x)=|\sin x|$, then
A
$f$ is everywhere differentiable
B
$f$ is everywhere continuous but not differentiable at $x=n \pi, n \in Z$
C
$f$ is everywhere continuous but not differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$
D
None of the above