56
MCQ (Single Correct Answer)
$\lim _\limits{x \rightarrow 0} \frac{(1+x)^n-1}{x}$ is equal to
A
$n$
B
1
C
$-n$
D
0
57
MCQ (Single Correct Answer)
$\lim _\limits{x \rightarrow 1} \frac{x^m-1}{x^n-1}$ is equal to
A
1
B
$\frac{m}{n}$
C
$-\frac{m}{n}$
D
$\frac{m^2}{n^2}$
58
MCQ (Single Correct Answer)
$\lim _\limits{\theta \rightarrow 0} \frac{1-\cos 4 \theta}{1-\cos 6 \theta}$ is equal to
A
$\frac{4}{9}$
B
$\frac{1}{2}$
C
$\frac{-1}{2}$
D
$-1$
59
MCQ (Single Correct Answer)
$\lim _\limits{x \rightarrow 0} \frac{\operatorname{cosec} x-\cot x}{x}$ is equal to
A
$\frac{-1}{2}$
B
1
C
$\frac{1}{2}$
D
1
60
MCQ (Single Correct Answer)
$\lim _\limits{x \rightarrow 0} \frac{\sin x}{\sqrt{x+1}-\sqrt{1-x}}$ is equal to
A
2
B
0
C
1
D
$-$1