Limits Continuity And Differentiability Question 97
Question: The value of f(0) so that the function $ f(x)=\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x} $ is continuous at each point in its domain, is equal to
Options:
A) 2
B) 1/3
C) 2/3
D) -1/3
Show Answer
Answer:
Correct Answer: B
Solution:
The function f is clearly continuous at each point in its domain except possibly at x=0.
Given that f(x) is continuous at x=0.
$ \therefore f(0)=\underset{x\to 0}{\mathop{\lim }}f(x) $
$ =\underset{x\to 0}{\mathop{\lim }}\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x} $
$ =\underset{x\to 0}{\mathop{\lim }}\frac{2-(si{n^{-1}}x)/x}{2+({{\tan }^{-1}}x)x}=\frac{1}{3} $
BETA
