Chapter 14.2, Problem 13AYU

To determine

To find: The value of the given limit.

Answer to Problem 13AYU

The value of the limit is $80$ .

Explanation of Solution

Given:

The given limit is $\underset{x\to 2}{\lim }\left(5x^4\right)$

Calculation:

Consider the given limit is,

  $\underset{x\to 2}{\lim }\left(5x^4\right)$

Then, solve the limit as,

  $\underset{x\to 2}{\lim }\left(5x^4\right)=\left[\underset{x\to 2}{\lim }\left(5\right)\right]\left[\underset{x\to 2}{\lim }{x}^4\right]$

Consider the function as,

  $\underset{x\to c}{\lim }f\left(x\right)\cdot g\left(x\right)=\left[\underset{x\to c}{\lim }f\left(x\right)\right]\left[\underset{x\to c}{\lim }g\left(x\right)\right]$

Then,

  $\begin{array}{c}\underset{x\to 2}{\lim }\left(5x^4\right)=\left[5\right]\left[2^4\right]\\ =80\end{array}$