Chapter 14.2, Problem 28AYU

To determine

To find: The value of limit $\underset{x\to -1}{\lim }{\left(2x+1\right)}^{5/3}$ .

Answer to Problem 28AYU

The value of limit $\underset{x\to -1}{\lim }{\left(2x+1\right)}^{5/3}$ is $-1$ .

Explanation of Solution

Given:

The function is $\underset{x\to -1}{\lim }{\left(2x+1\right)}^{5/3}$ .

Calculation:

Simplify the expression as follows.

  $\begin{array}{c}\underset{x\to -1}{\lim }{\left(2x+1\right)}^{5/3}={\left(2\left(-1\right)+1\right)}^{5/3}\\ ={\left(-2+1\right)}^{5/3}\\ ={\left(-1\right)}^{5/3}\\ =-1\end{array}$

Hence, the value of limit $\underset{x\to -1}{\lim }{\left(2x+1\right)}^{5/3}$ is $-1$ .