Functions Question 129

Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{1-\cos 6x}{x}= $

[DSSE 1982]

Options:

A) 0

B) 6

C) $ \frac{1}{3} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

$ \underset{x\to 0}{\mathop{\lim }}\frac{1-\cos 6x}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{2{{\sin }^{2}}3x}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{x,.,2{{\sin }^{2}}3x}{x^{2}}=0 $ .