Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 3

Answer

(a) Look and see what happens to y as x goes to -3 from both the left and right hand side. y goes to $\infty$. (b) Look and see what happens to y as x goes to 4 from the right hand side. y goes to $-\infty$.

Work Step by Step

(a) $\lim\limits_{x \to -3}$f(x)=$\infty$ There is no positive or negative sign to the right of -3 so that means x approaches -3 from both the left and right hand side. The negative sign in front of -3 is not to be confused with the negative/positive signs that show the direction of the limit. One is on the left while the other is on the right. f(x)=$\infty$ so y approaches $\infty$. (b) $\lim\limits_{x \to 4^+}$f(x)=$-\infty$ The $4^+$ means x is approaching 4 from the right hand side. f(x)=$-\infty$ so y goes to $-\infty$.
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