First slide

Continuity

Question

The value of $f (0)$ so that $f (x) = {(1 + 3 x)}^{\frac{1}{x}}$ is continuous at $x = 0$ is

Easy

A

$e^{2}$
B

$e^{3}$
C

$e^{5}$
D

$e^{7}$

Solution

$\underset{x \to 0}{L t} f (x) = f (0)$ $\lim_{x \to c} f {(x)}^{g (x)} \to 1^{\infty} t h e n \lim_{x \to c} f {(x)}^{g (x)} = e^{\lim_{x \to c} g (x) {f (x) - 1}}$
= $\lim_{x \to 0} {(1 + 3 x)}^{\frac{1}{x}} = e^{\lim_{x \to 0} \frac{1}{x} (1 + 3 x - 1)}$
$\Rightarrow f (0) = e^{3}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App