Pre-Calc Homework Solutions 96

# Pre-Calc Homework Solutions 96 - 96 Section 3.6 d u du u(u...

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Unformatted text preview: 96 Section 3.6 d u du u (u 1 1 1 (u 1 d (x 2 dx 1 2 1 1) u u 1) 1 d u 1 du u (u 1) 1 1 d (u du 38. f (u) u 2 u u 2 u 2 41. 1) dx dt dy dt dy dx d (2 cos t) dt d (2 sin t) dt dy dt dx dt 2 sin t 2 cos t cot t d (u du 1) (u (u 1)2 (u 1) 4(u 1) 1)2 (u 1)3 2 cos t 2 sin t g (x) 1) 2x 3 The line passes through 2 cos and has slope y (x cot 2) 4 4 , 2 sin 4 ( 2, 2) ( f g) ( 1) f (g( 1))g ( 1) f (0)g ( 1) ( 4)(2) 8 42. 2) 1. Its equation is 2, or y x 2 2. 39. (a) dy dx dy du du dx d d (cos u) (6x du dx dx dt dy dt dy dx d (sin 2 t) dt d (cos 2 t) dt dy dt dx dt (cos 2 t) (2 t) ( sin 2 t) (2 t) tan 2 t 2 6 2 d dt d dt 2 cos 2 t 2 sin 2 t ( sin u)(6) 6 sin u 6 sin (6x (b) dy dx 2 sin 2 t 2 cos 2 t 2) The line passes through sin 2 , cos dy du du dx d d (cos 2u) (3x du dx 6 2 3 1 , 2 and has slope 1) y 43. dx dt tan 3 2 3 x d (sec 2 t dt ( sin 2u)(2) (3) 6 sin 2u 6 sin (6x dy 40. (a) dx dy du du dx d sin (u du 6 1 , or y 2 3. Its equation is 3x d dt 2. 1) (2 sec t) (sec t) (2 sec t)(sec t tan t) 2 sec 2 t tan t 2) d 1) (x 2) dx dy dt dy dx d tan t dt dy dt dx dt sec 2 t 1 cot t. 2 cos (u 2x cos (u 1)(1) 2x 1) 1) sec2 t 2 sec2 t tan t 2x cos (x 2 dy (b) dx The line passes through sec 2 4 1 cot 2 1 (x 2 d sec t dt d tan t dt dy dt dx dt 1, tan 4 dy du du dx d d (sin u) (x 2 du dx 4 (1, 1) and has slope 1) y 44. dx dt dy dt dy dx 1 . Its equation is 2 (cos u)(2x) 2x cos u 2x cos (x 2 1) 1, or y sec t tan t sec 2 t sec t tan t 1 x 2 1 . 2 1) sec 2 t sec t tan t 1 sin t csc t 2 6 3 1 3 2 3 1 3 The line passes through sec has slope csc or y 2x 6 , tan , and , 6 2. Its equation is y 3. 2 x ...
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