Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 13 - Section 13.2 - Finding Limits Algebraically - 13.2 Exercises: 21

Answer

$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$ doesn't exist.

Work Step by Step

$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$ Try to find the limit applying direct substitution: $\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}=\dfrac{(-2)^{2}-(-2)+6}{-2+2}=\dfrac{4+2+6}{0}=\infty$ $\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$ doesn't exist.
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