Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 67: 41


$\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}=3$

Work Step by Step

$\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}$ Take out common factor $x$ in the numerator and simplify: $\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}=\lim\limits_{x \to 0}\dfrac{x(x+3)}{x}=\lim\limits_{x \to 0}x+3=...$ Apply direct substitution to evaluate the limit: $\lim\limits_{x \to 0}x+3=0+3=3$
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