84
MCQ (Single Correct Answer)
The function $f(x)=\frac{4-x^2}{4 x-x^3}$ is
A
discontinuous at only one point
B
discontinuous at exactly two points
C
discontinuous at exactly three points
D
None of the above
85
MCQ (Single Correct Answer)
The set of points where the function $f$ given by $f(x)=|2 x-1| \sin x$ is differentiable is
A
$R$
B
$R-\left(\frac{1}{2}\right)$
C
$(0, \infty)$
D
None of these
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