Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises: 3

Answer

$\lim\limits_{x \to 3}(5x^3-3x^2+x-6)=105$

Work Step by Step

$\lim\limits_{x \to 3}(5x^3-3x^2+x-6)$ $=\lim\limits_{x \to 3}5x^3-\lim\limits_{x \to 3}3x^2+\lim\limits_{x \to 3}x-\lim\limits_{x \to 3}6$ (sum and difference law) $=5\lim\limits_{x \to 3}x^3-3\lim\limits_{x \to 3}x^2+\lim\limits_{x \to 3}x-6$ (constant multiple law and $\lim\limits_{x \to a}c=c$) $=5\times3^3-3\times3^2+3-6$ (direct substitution property) $=105$
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