Chapter 11, Problem 16RE

To determine

To Calculate:

The limit by using direct substitution.

Answer to Problem 16RE

The limit $\underset{x\to -1}{\lim }\sqrt{5-x}$ is $\sqrt{6}$ .

Explanation of Solution

Given Information:

  $\underset{x\to -1}{\lim }\sqrt{5-x}$

Calculation:

To get the limit of the function use direct substitution method, replace the value of $x$ by the default values.

Use properties of limit $\underset{x\to 0}{\lim }{\left[f\left(x\right)\right]}^n={\left[\underset{x\to 0}{\lim }f\left(x\right)\right]}^n$

Therefore,

  $\begin{array}{l}\underset{x\to -1}{\lim }\sqrt{5-x}=\sqrt{\underset{x\to -1}{\lim }-\underset{x\to -1}{\lim x}}\\ =\sqrt{5-\underset{x\to -1}{\lim x}}\end{array}$

Replace $x$ by $-1$

  $\begin{array}{l}\underset{x\to -1}{\lim }\sqrt{5-x}=\sqrt{5-\left(-1\right)}\\ =\sqrt{5+1}\\ =\sqrt{6}\end{array}$

Hence, the limit of function $\underset{x\to -1}{\lim }\sqrt{5-x}$ is $\sqrt{6}$ .