Chapter 2.3, Problem 1E

To determine

To find the limit (if it exists)

  $\underset{x\to \sqrt{2}}{\lim }15$

Answer to Problem 1E

  $\underset{x\to \sqrt{2}}{\lim }15=15$

Explanation of Solution

Given:

  $\underset{x\to \sqrt{2}}{\lim }15$

Concept Used:

One theorem on limits suggest that limit of a constant function at any point is always that constant value; that is,

  $\underset{x\to a}{\lim }c=c$ , where $c$ is any constant.

Calculation:

To find the limit (if it exists)

  $\underset{x\to \sqrt{2}}{\lim }15$

First note that 15 is constant number, and theorem on limits of a constant function implies that

  $\underset{x\to a}{\lim }c=c$ , where $c$ is an constant

Thus,

  $\underset{x\to a}{\lim }15=15$

For any real number a.

Hence,

  $\underset{x\to \sqrt{2}}{\lim }15=15$