66
MCQ (Single Correct Answer)
$\lim _{x \rightarrow 0} \frac{\tan 2 x-x}{3 x-\sin x}$ is equal to
A
2
B
$\frac{1}{2}$
C
$\frac{-1}{2}$
D
$\frac{1}{4}$
67
MCQ (Single Correct Answer)
If $f(x)=x-[x], \in R$, then $f^{\prime}\left(\frac{1}{2}\right)$ is equal to
A
$\frac{3}{2}$
B
1
C
0
D
$-1$
68
MCQ (Single Correct Answer)
If $y=\sqrt{x}+\frac{1}{\sqrt{x}}$, then $\frac{d y}{d x}$ at $x=1$ is equal to
A
1
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
D
0
69
MCQ (Single Correct Answer)
If $f(x)=\frac{x-4}{2 \sqrt{x}}$, then $f^{\prime}(1)$ is equal to
A
$\frac{5}{4}$
B
$\frac{4}{5}$
C
1
D
0
70
MCQ (Single Correct Answer)
If $y=\frac{1+\frac{1}{x^2}}{1-\frac{1}{x^2}}$, then $\frac{d y}{d x}$ is equal to
A
$\frac{-4 x}{\left(x^2-1\right)^2}$
B
$\frac{-4 x}{x^2-1}$
C
$\frac{1-x^2}{4 x}$
D
$\frac{4 x}{x^2-1}$