Chapter 2.6, Problem 1E

To determine

The limit of the expression $\underset{x\to 3}{\lim }\frac{5x+11}{\sqrt{x+1}}$ .

Answer to Problem 1E

The limit of the expression $\underset{x\to 3}{\lim }\frac{5x+11}{\sqrt{x+1}}$ is 13.

Explanation of Solution

Given:

The expression is $\underset{x\to 3}{\lim }\frac{5x+11}{\sqrt{x+1}}$ .

Calculation:

Substitute 3 for $x$ in expression $\underset{x\to 3}{\lim }\frac{5x+11}{\sqrt{x+1}}$ to obtain the value of the limit as follows:

  $\begin{array}{c}\frac{5\left(3\right)+11}{\sqrt{3+1}}=\frac{15+11}{\sqrt{4}}\\ =\frac{26}{2}\\ =13\end{array}$

Thus, the limit of the expression $\underset{x\to 3}{\lim }\frac{5x+11}{\sqrt{x+1}}$ is 13.