Chapter 12, Problem 17RE

To determine

To Find: The limit $\underset{x\to -1}{\lim }\sqrt{5-x}$ by direct substitution.

Answer to Problem 17RE

  $\underset{x\to -1}{\lim }\sqrt{5-x}=\sqrt{6}$

Explanation of Solution

Given information:

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

Concept and Formula Used:

To find the limit by direct substitution put the value of limit given in variable of a function.

Calculation:

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

Putting the value of $x=-1$ in the limit.

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

Conclusion:

  $\underset{x\to -1}{\lim }\sqrt{5-x}=\sqrt{6}$