Chapter 11.1, Problem 67E

To determine

To calculate:

The limit of the following by direct substitution:

  $\underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)$

Answer to Problem 67E

The limit of $\underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)$ is $0$ .

Explanation of Solution

Given information:

  $\underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)$

Calculation:

The function is given as:

  $\underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)$

Use the direct substitution method to find the value of the given function:

  $\begin{array}{l}\underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)=\left(\frac{2\left(0\right)}{\sqrt{0+16}}\right)\left[\because x=0\right]\\ \underset{x\to 0}{\lim }\left(\frac{2x}{\sqrt{x+16}}\right)=0\end{array}$