Calculus 8th Edition

Published by Cengage

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 5

Answer

(a) 2 (b) 1 (c) 4 (d) does not exist because $\lim\limits_{x \to 3^-}$$\ne$$\lim\limits_{x \to 3^+}$ (e) 3

Work Step by Step

(a) As x approaches 1 from both the left and right hand side f(x) goes to 2. (b) As x approaches 3 from the left hand side, f(x) goes to 1. (c) As x approaches 3 from the right hand side, f(x) goes to 4. (d) $\lim\limits_{x \to 3}$ does not exist because $\lim\limits_{x \to 3^-}$$\ne$$\lim\limits_{x \to 3^+}$. They must go to the same number for $\lim\limits_{x \to 3}$ to exist. (e) There is a point at (3,3) on the graph so f(3)=3.

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