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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Limits

NDA 2018 · Mathematics · Limits

If the function f(x)= 2 x- ^ -1 x 2 x+ ^ -1 x is continuous at each...

If the function f(x)=2x−sin⁡−1x2x+tan⁡−1xf(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} is continuous at each point in its domain, then what is the value of f(0)f(0) ?

Options

  1. A-1/3
  2. B1/3
  3. C2/3
  4. D2

Correct answer

B. 1/3

Step-by-step solution

f(0)=lim⁡x→02x−sin⁡−1x2x+tan⁡−1x=lim⁡x→02−sin⁡−1xx2+tan⁡−1xx=2−12+1=13\begin{aligned} & f(0)=\lim _{x \rightarrow 0} \frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \\ & =\lim _{x \rightarrow 0} \frac{2-\frac{\sin ^{-1} x}{x}}{2+\frac{\tan ^{-1} x}{x}}=\frac{2-1}{2+1}=\frac{1}{3}\end{aligned}
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