Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 35

Answer

$ -\infty$

Work Step by Step

$x\rightarrow(\pi/2)^{+}$ means that x approaches $\displaystyle \frac{\pi}{2}$ from the right (the greater side), it is positive, so $\displaystyle \frac{1}{x}$ is positive. Secant and cosine are reciprocal. The cosine (and secant) of x, belonging (slightly) to quadrant II, are negative. Since $\cos x$ approaches 0 from the negative side, $\sec x\rightarrow-\infty$ So, as $x\rightarrow(\pi/2)^{+}$ the product ($\displaystyle \frac{1}{x}\sec x$) $\rightarrow-\infty$.
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