Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Review Exercises - Page 1179: 46


Continuous at $ x=a $

Work Step by Step

Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$. $\lim_\limits{x \to a} f(x)= \lim_\limits{x \to a}(x^3+5x-1)=a^3+5a^2-1$ So, $\lim_\limits{x \to a} f(x)$ exists. Now, $\lim_\limits{x \to a} f(x)=a^3+5a^2-1$ and $ f(a)=a^3+5a^2-1$ so, $\lim_\limits{x \to a} f(x) =f(a)$ Therefore, the function is continuous at $ x=a $
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