Find the limits x + 2lim-2 Vx + 5- 3

Given limits: limx→-2 x+2x2+5-3

Answered: x + 2 lim -2 Vx + 5- 3

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter2: Equations And Inequalities

Section: Chapter Questions

Problem 7PT: Solve for x:3(2x5)3(x7)=2x9.

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Question

Find the limits

Expert Solution

Step 1

Given limits:

$\lim_{x \to - 2} \frac{x + 2}{\sqrt{x^{2} + 5} - 3}$

Step 2

Rationalize the denominator, we get

$\lim_{x \to - 2} \frac{x + 2}{\sqrt{x^{2} + 5} - 3} \times \frac{\sqrt{x^{2} + 5} + 3}{\sqrt{x^{2} + 5} + 3} \lim_{x \to - 2} \frac{(x + 2) (\sqrt{x^{2} + 5} + 3)}{{(\sqrt{x^{2} + 5})}^{2} - 3^{2}} \lim_{x \to - 2} \frac{(x + 2) (\sqrt{x^{2} + 5} + 3)}{x^{2} + 5 - 9} \lim_{x \to - 2} \frac{(x + 2) (\sqrt{x^{2} + 5} + 3)}{x^{2} - 4} \lim_{x \to - 2} \frac{(x + 2) (\sqrt{x^{2} + 5} + 3)}{x^{2} - 2^{2}} \lim_{x \to - 2} \frac{(x + 2) (\sqrt{x^{2} + 5} + 3)}{(x - 2) (x + 2)} \lim_{x \to - 2} \frac{(\sqrt{x^{2} + 5} + 3)}{(x - 2)}$

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