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Unformatted text preview: 114 Section 3.8 22. continued (c) At the points x (d)
2 y (b) y k , where k is an odd integer.
2 2 d sec 1 x dx x (c) None, since 30. (a) y (b) y 0 0 1 x2 1 0. (c) None, since
x d csc 1 x dx
1 1 x x2 1 0. 2 2 31. (a) None, since sin undefined for x (b) None, since sin x is 1. x is undefined for x
1 1 x2 1 1. 0. 1. 1. 0. 2 (c) None, since d sin 1 x dx
1 1 (e) f (x) d sin 1 (sin x) dx d sin x 1 sin2 x dx cos x 1 sin2 x 1 32. (a) None, since cos (b) None, since cos (c) None, since 33. (a)
1 x x is undefined for x x is undefined for x
1 1 x2 d cos 1 x dx which is 1 depending on whether cos x is positive or negative. cos 23. (a) v(t) (b) a(t) (c) 24.
2 d dx 2 dx dt dv dt 1 1 t2 2t which is always negative. (1 t 2)2 1 1 x, sin sin
1 1 x
2 which is always positive. So cos (b) x x . x d cos 1 (x) dx sin 1 x tan So tan (c) 1
1 1 0 d sin 1 (x) dx 1 1 x2 x, cot cot
1 1 x
2 x x . x 1 25. d cot 1 x dx d tan 1 (x) dx 2 d 0 tan 1 (x) dx 1 1 x2 sec So sec 34.
1 1 x, csc csc
1 1 x
2 x x . d 26. csc 1 (x) dx d dx 2 sec 1 (x) 0
x d sec 1 (x) dx 1 x
2 A B C 1 27. (a) y (b) y 2 2 d tan 1 x dx 1 1 x2 (c) None, since 28. (a) y (b) y (c) None, since 29. (a) y
2 0. 0
d cot 1 x dx 1 1 x2 0. The "straight angle" with the arrows in it is the sum of the three angles A, B, and C. A is equal to tan 1 3 since the opposite side is 3 times as long as the adjacent side. B is equal to tan 1 2 since the side opposite it is 2 units and the adjacent side is one unit. C is equal to tan 1 1 since both the opposite and adjacent sides are one unit long. But the sum of these three angles is the "straight angle," which has measure radians. ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.
 Fall '08
 GERMAN

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