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 - Page 59: 1


$\lim\limits_{x \to 2}$f(x)=5 Look and see what happens to y as x goes to 2 from the left and right hand side. y goes to 5. Yes, it is possible for this statement to be true and yet f(2)=3.

Work Step by Step

When we first see the limit, we see that x goes to 2. Because there isn't a positive or negative sign to the right of the 2, that means it goes to 2 from both the left and right hand side. f(x)=5 means y goes to 5. It is possible for $\lim\limits_{x \to 2}$f(x)=5 to be true and have f(2)=3 because the very definition of a limit means x approaches the 2, but is never actually 2. That means f(2) can be anything as long as it approaches 5. 3 approaches 5; therefore; it is possible.
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