Answers - Answers to Selected Exercises Chapter 1 1....

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Unformatted text preview: Answers to Selected Exercises Chapter 1 1. second, fifth, fifth, forty-second 3a i. yes, it is 3a ii. no, it is not 3a iii. no 3b i. no 3b ii. yes 3b iii. no 3c i. yes 3c ii. no 3c iii. no 3d i. no 3d ii. no 3d iii. yes 3e i. no 3e ii. yes 3e iii. yes 3f i. no 3f ii. no 3f iii. yes 3g i. no 3g ii. yes 3g iii. yes 3h i. yes 3h ii. yes 3h iii. yes 4a i. no 4a ii. yes 4a iii. no 4b i. no 4b ii. no 4b iii. yes 4c i. yes 4c ii. no 4c iii. no 4d i. no 4d ii. no 4d iii. yes 5b i. 9 5b ii. 5 5c i. y = radicalbig x 2 + 9 5c ii. y = radicalbig x 2 + 5 6b i. y = 4 e x 2 − 3 6b ii. y = 3 e x 2 − 1 − 3 7b i. y = 3 cos ( 2 x ) + 4 sin ( 2 x ) 7b ii. y = 1 2 sin ( 2 x ) 8a i. 7 8a ii. No, because then 7 = y ′ ( 1 ) = 4 . 8a iii. d 2 y dx 2 = 3 x dy dx + 3 y + 2 x , y ′′ ( 1 ) = 29 8a iv. Of course. 8b i. y ′′ ( ) = 4 and y ′′′ ( ) = 24 8b ii. No. 9a. 100 / 7 sec. 9b. − 140 meters/second 9c i. y ′ ( ) = 0 is replaced with y ′ ( ) = 2 9c ii. − 4 . 9 t 2 + 2 t + 1000 9c iii. − 2 √ 4901 meters/second 10a. d v / dt = − 9 . 8 − κ(v − 2 ) 10b i. 1000 κ 10b ii. (v hit + 9 . 8 t hit ) / 1000 11b. 3 x + 5 x ln | x | 11c. Because y ( x ) is not continuous at x = 0 . Chapter 2 2a. Yes, it is directly integrable. 2b. No, it is not directly integrable. 2c. No 2d. Yes 2e. No 2f. Yes 2g. Yes 2h. No 2i. No 3a. x 4 + c 3b. − 5 e − 4 x + c 3c. 2 ln | x | − 2 √ x + c 3d. 2 √ x + 4 + c 3e. 1 2 sin ( x 2 ) + c 3f. x sin ( x ) + cos ( x ) + c 3g. 1 2 ln vextendsingle vextendsingle x 2 − 9 vextendsingle vextendsingle + c 3h. 1 6 ln vextendsingle vextendsingle vextendsingle vextendsingle x − 3 x + 3 vextendsingle vextendsingle vextendsingle vextendsingle + c 3i. 1 27 x 3 − 1 9 x + c 3j. − 1 4 sin ( 2 x ) + c 1 x + c 2 3k. 1 6 x 3 + 3 2 x 2 + c 1 x + c 2 3l. 1 24 x 4 + c 1 x 3 + c 2 x 2 + c 3 x + c 4 4a. 2 x 2 + 5 e 2 x − 1 for − ∞ < x < ∞ 4b. 3 2 ( x + 6 ) 2 / 3 + 4 for − ∞ < x < ∞ 4c. x − 2 ln | x + 1 | + 8 for − 1 < x < ∞ 4d. 2 √ x − 2 ln | x | + 4 for < x < ∞ 4e. − ln | cos ( x ) | + 3 for − π 2 < x < π 2 4f. arctan ( x ) + 3 for − ∞ < x < ∞ 4g. − 2 x ln | x | + 4 3 √ x 3 + 6 x + 2 3 for < x < ∞ 5a. − 2 cos parenleftBig x 2 parenrightBig + 2 + y ( ) 5b i. 2 5b ii. 5 5b iii. 7 6a. 2 ( x + 3 ) 3 / 2 + y ( 1 ) − 16 6b i. 54 6b ii. 50 607 608 Answers to Selected Exercises 6b iii. − 13 7a. 7 2 − 1 2 e − x 2 7b. 4 + radicalbig x 2 + 5 7c. arctan x − π 2 7d. π 6 erf ( 3 x ) + 1 7e. Si ( x ) + 4 7f. 1 2 Si ( x 2 ) ) 9a. braceleftBigg if x < x if ≤ x bracerightBigg 9b. braceleftBigg 2 if x < 1 x + 1 if 1 ≤ x bracerightBigg 9c. if x < 1 x − 1 if 1 ≤ x ≤ 2 1 if 2 < x 9d....
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Answers - Answers to Selected Exercises Chapter 1 1....

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