Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 14



Work Step by Step

Given $$ \lim _{t\rightarrow \infty}\frac{t-t\sqrt{t} }{2t^{3/2}+3t-5}$$ Then \begin{aligned} \lim _{t\rightarrow \infty}\frac{t-t\sqrt{t} }{2t^{3/2}+3t-5} &= \lim _{t\rightarrow \infty}\frac{\frac{t}{t^{3/2}}-\frac{t\sqrt{t}}{t^{3/2}}}{\frac{2t^{3/2}}{t^{3/2}}+3\frac{t}{t^{3/2}}-\frac{5}{t^{3/2}}} \\ &= \lim _{t\rightarrow \infty}\frac{\frac{1}{t^{1/2}}-1}{2+\frac{3}{t^{1/2}}-\frac{5}{t^{3/2}}} \\ &= \lim _{t\rightarrow \infty}\frac{0-1 }{2+0-0}\\ &=\frac{-1}{2} \end{aligned}
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