Question

In Problems 7– 42, find each limit algebraically.

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

Short answer

The answer is -1.

Step-by-step solution

Step. 1 Given Information

Given is the limit on which x tends to -1 and the function given is:

${\left(2x+3\right)}^{5/3}$

Step. 2 Solving the limit

Firstly, we check whether the given function is in indeterminant form or not.

Since if we put $x=-1$ then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function. So,

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