Question

In Problems 7– 42, find each limit algebraically.

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

Short answer

The answer is 32.

Step-by-step solution

Step. 1 Given Information

Given is the limit on which x tends to 2 and the function given is:

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

Step. 2 Solving the limit

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

Since if we put $x=2$ then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function.

$$\begin{gathered} \underset{x\to 2}{\lim }{\left(3x-2\right)}^{5/2}={\left(3\left(2\right)-2\right)}^{5/2} \\ ={\left(6-2\right)}^{5/2} \\ =4^{5/2} \\ ={\left(\sqrt{4}\right)}^5 \\ =2^5=32. \end{gathered}$$