First slide

Introduction to limits

Question

$lim_{x \to a} \frac{(x + 2)^{5 / 3} - (a + 2)^{5 / 3}}{x - a}$ is equal to

Easy

A

$\frac{5}{3} (a + 2)^{2 / 3}$
B

$\frac{3}{5} (a + 3)^{5 / 3}$
C

$\frac{3}{5} (a + 3)^{1 / 2}$
D

$\frac{5}{3} (a + 2)^{3 / 2}$

Solution

$\begin{array}{l} lim_{x \to a} \frac{(x + 2)^{5 / 3} - (a + 2)^{5 / 3}}{x - a} \\ = lim_{x \to a} \frac{(x + 2)^{5 / 3} - (a + 2)^{5 / 3}}{(x + 2) - (a + 2)} = lim_{x \to a} \frac{y^{5 / 3} - b^{5 / 3}}{y - b} \end{array}$
where x+2=y and a+2=b
$= \frac{5}{3} b^{5 / 3 - 1} = \frac{5}{3} b^{2 / 3} = \frac{5}{3} (a + 2)^{2 / 3}$

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