Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises: 53

Answer

\[ = \frac{3}{4}\]

Work Step by Step

\[\begin{gathered} \mathop {\lim }\limits_{x \to 0} \,\,\frac{{3{{\sec }^5}x}}{{{x^2} + 4}} \hfill \\ \hfill \\ let\,\,x = 0\,\, \hfill \\ \hfill \\ then \hfill \\ \hfill \\ = \frac{{3\,{{\sec }^5}\,\left( 0 \right)}}{{\,{{\left( 0 \right)}^2} + 4}} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{{3\,\left( 1 \right)}}{{0 + 4}} \hfill \\ \hfill \\ = \frac{3}{4} \hfill \\ \hfill \\ \end{gathered} \]
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