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(Answers to Exercises for Chapter 8: Inverse Trig and Hyperbolic Functions) A.8.1 CHAPTER 8: INVERSE TRIG and HYPERBOLIC FUNCTIONS SECTION 8.1: INVERSE TRIG FUNCTIONS 1) a) ± 6 b) ± ² 3 c) undefined d) 3 4 e) ± 4 f) 5 g) 5 6 2) a) x 25 ± x 2 , or x 25 ± x 2 25 ± x 2 b) 1 x 2 + 1 , or x 2 + 1 x 2 + 1

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(Answers to Exercises for Chapter 8: Inverse Trig and Hyperbolic Functions) A.8.2 SECTION 8.2: CALCULUS and INVERSE TRIG FUNCTIONS 1) a) 1 2 x 1 + x () , or x 2 x 1 + x b) 2 x arcsin 3 x + 3 x 2 1 ± 9 x 2 , or 1 ± 9 x 2 2 x 1 ± 9 x 2 arcsin 3 x + 3 x 2 ² ³ ´ µ · 1 ± 9 x 2 c) ± 1 x ± ln x 2 d) 5 e t + arcsec t 4 ± ² ³ ´ 4 e t + 4 tt 8 µ 1 ± ² ³ ´ · · · , or 5 e t + arcsec t 4 ± ² ³ ´ 4 te t t 8 µ 1 + 4 8 µ 1 e) 1 1 + x 2 ± arctan x 2 2) a) and b) 1. In a), use inverse properties. Observe that arcsin sin x = x if ± ² 2 < x < 2 . Note: There are other real values of x for which arcsin sin x ± x ; for example, consider x = 5 ± 6 . In b), observe that ± sin 2 x = cos 2 x = cos x = cos x , because ± 2 < x < 2 .
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