Precalculus (6th Edition) Blitzer

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

Chapter 11 - Section 11.2 - Finding Limits Using Properties of Limits - Exercise Set - Page 1153: 27



Work Step by Step

Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$. In order to to find the limit, we will plug $ a $ into the function and then simplify. $\lim_\limits{x\to 2} \dfrac{x^3-2x^2+4x-8}{x^4-2x^3+x-2}=\dfrac{\lim_\limits{x\to 2} (x^2+4) (x-1)}{\lim_\limits{x\to 2} (x-2)(x+1)(x^2-x+1)}=\lim_\limits{x\to 2} \dfrac{x^2+4}{(x+1)(x^2-x+1)}=\dfrac{8}{3 \cdot 3}=\dfrac{8}{9}$
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