In order that the function f (x)=(x+1)^ 1 x is continuous at x=0,… - Vidyadip

MCQ

In order that the function $f (x)=(x+1)^{\frac{1}{x}}$ is continuous at $x=0, f (0)$ must be defined as

A
$f(0)=0$
✓
$f(0)=e$
C
$f(0)=\frac{1}{e}$
D
$f(0)=1$

✓

Answer

Correct option: B.

$f(0)=e$

(B)
For $f (x)$ to be continuous at $x=0$,
$f (0)=\lim _{x \rightarrow 0} f (x)=\lim _{x \rightarrow 0}(1+x)^{\frac{1}{x}}= e$

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