MCQ
If $f (x)=\left\{\begin{array}{cl}\left(1+\frac{4 x}{5}\right)^{\frac{1}{x}}, & x \neq 0 \\ e ^{\frac{4}{5}}, & x=0\end{array}\right.$, then
  • A
    $\lim _{x \rightarrow 0} f(x)=e^{\frac{2}{5}}$
  • B
    $\lim _{x \rightarrow 0} f(x)$ does not exist
  • $f (x)$ is continuous at $x=0$
  • D
    $f (x)$ is discontinuous at $x=0$

Answer

Correct option: C.
$f (x)$ is continuous at $x=0$
(C)
$\lim _{x \rightarrow 0} f (x)=\lim _{x \rightarrow 0}\left(1+\frac{4 x}{5}\right)^{\frac{1}{x}}$
$=\left[\lim _{x \rightarrow 0}\left(1+\frac{4 x}{5}\right)^{\frac{5}{4 x}}\right]^{\frac{4}{5}}= e ^{\frac{4}{5}}= f (0)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free