Functions Question 678
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{x^{3}\cot x}{1-\cos x}= $
[AI CBSE 1988; DSSE 1988]
Options:
A) 0
B) 1
C) 2
D) ?2
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{x^{3}\cot x}{1-\cos x}=\underset{x\to 0}{\mathop{\lim }}( \frac{x^{3}\cot x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} ) $ $ =\underset{x\to 0}{\mathop{\lim }}{{( \frac{x}{\sin x} )}^{3}}\times \underset{x\to 0}{\mathop{\lim }}\cos x\times \underset{x\to 0}{\mathop{\lim }}(1+\cos x)=2 $
BETA
