## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 11

#### Answer

Prove that $\lim\limits_{x\to-1}f(x)=f(-1)$

#### Work Step by Step

*NOTES TO REMEMBER: $f(x)$ is continuous at $a$ if and only if $$\lim\limits_{x\to a}f(x)=f(a)$$ We consider $\lim\limits_{x\to-1}f(x)$ $=\lim\limits_{x\to-1}(x+2x^3)^4$ $=(\lim\limits_{x\to-1}(x+2x^3))^4$ $=(\lim\limits_{x\to-1}x+2\lim\limits_{x\to-1}(x^3))^4$ $=(-1+2\times(-1)^3)^4$ $=f(-1)$ Therefore, $f(x)$ is continuous at $-1$.

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