Q95 / 170 · Manipal (MET) 2017 · Mathematics

If $f(x)=\frac{3 x+\tan ^2 x}{x}$ is continuous at $x=0$, then $f(0)$ is equal to

  • Correct answer
    A
    3
  • B
    2
  • C
    4
  • D
    0

Solution

Now, $\begin{aligned} \lim _{x \rightarrow 0} f(x) & =\lim _{x \rightarrow 0} \frac{3 x+\tan ^2 x}{x} \\ & =\lim _{x \rightarrow 0} \frac{3+2 \tan x \sec ^2 x}{1} \\ & =3 \end{aligned}$ Since, $f(x)$ is continuous at $x=0$ $\therefore f(0)=3$

Hence, the correct answer is option: 'A'.

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