Answered: One-sided limits a. Evaluate lim Vx -…

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One-sided limits a. Evaluate lim Vx - 2. xS2+ b. Explain why lim Vx - 2 does not exist. xS2-

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section: Chapter Questions

Problem 6SGR

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Question

One-sided limits
a. Evaluate lim Vx - 2.
xS2+
b. Explain why lim Vx - 2 does not exist.
xS2-

Expert Solution

Step 1

We know that a function $f (x) = \sqrt{x}$ is defined if $x \geq 0$ .

a. We have to evaluate $\lim_{x \to 2^{+}} \sqrt{x - 2}$

Here $x \to 2^{+}$ it means that $x$ is slightly greater than 2.

So,

$x - 2 = 2^{+} - 2 > 0$

Therefore, function will be defined.

$\begin{array}{rcl} \lim_{x \to 2^{+}} \sqrt{x - 2} & = & \sqrt{2 - 2} \\ = & 0 \end{array}$

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