Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 4


$$\lim _{t \rightarrow 9} \frac{2 t-18}{5 t-45} =\frac{2}{5} $$

Work Step by Step

Given $$\lim _{t \rightarrow 9} \frac{2 t-18}{5 t-45}$$ let $$ f(t) = \frac{2 t-18}{5 t-45}$$ Since, we have $$ f(9)=\frac{18-18}{45-45}=\frac{0}{0}$$ So, transform algebraically and cancel \begin{aligned} L&=\lim _{t \rightarrow 9} \frac{2 t-18}{5 t-45}\\ &=\lim _{t \rightarrow 9} \frac{2( t-9)}{5( t-9)}\\ &=\lim _{t \rightarrow 9} \frac{2}{5}\\ &=\frac{2}{5} \end{aligned}
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