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

MCQ

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

A
$f(0) = 0$
✓
$f(0) = e$
C
$f(0) = 1/e$
D
$f(0) = 1$

✓

Answer

Correct option: B.

$f(0) = e$

b
(b) $\mathop {\lim }\limits_{x \to 0} \,f(x) = f(0) = \mathop {\lim }\limits_{x \to 0} \,\,{(1 + x)^{1/x}} = e.$

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