A) 2
B) 1/3
C) 2/3
D) -1/3
Correct Answer: B
Solution :
[b] 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. \[\therefore f(0)=\underset{x\to 0}{\mathop{\lim }}\,f(x)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{2-(si{{n}^{-1}}x)/x}{2+({{\tan }^{-1}}x)x}=\frac{1}{3}\]
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