Pre-Calc Homework Solutions 402

Pre-Calc Homework Solutions 402 - 402 dy dx Section 10.1...

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Unformatted text preview: 402 dy dx Section 10.1 dy/dt dx/dt sec2 t sec t tan t 8. csc t 13. x t 2, y 1 t, so (t 2)2 t 2 dt 1 dt 1)3/2 1) 1 1 0 (a) Nowhere, since csc t never equals zero. (b) csc t is undefined when t k (k any integer). Then (x, y) (sec (k ), tan (k )) ( 1, 0). The points are (1, 0) and ( 1, 0). 9. dy dx dy/dt dx/dt 3t 2 Length 0 1 0 t t2 4 1 4 3t 2 4 3 2 2 3 8 3 3 3 1 2 (t 3 1 3/2 (2 3 (a) 4 3t 2 0 when t 2 2 2 3 2 3 . 3 2 2 3 2 3 0.609 Then (x, y) , , 4 8 3 14. x 8t cos t, y /2 0 8t sin t, so (8t cos t)2 (8t sin t)2 dt , Length which evaluates to (3.155, 3.079). (b) Nowhere, since 4 10. dy dx dy/dt dx/dt 3 cos t 3 sin t (0.845, 2 3.079) and /2 8t dt 0 3t is never undefined. cot t k (k any integer). 15. x y Length 4t 2 0 /2 2 sec t tan t sec2 t sec t tan t cos t sec t cos t, (a) cot t 0 when t sin t, so /3 2 Then (x, y) 2 ( 2, 1 (b) 3 cos 2 (sec t 0 /3 /3 cos t)2 1 dt ( sin t)2 dt k ,1 3 sin 2 k 2). sec2 t tan t dt /3 0 0 3). The points are ( 2, 4) and ( 2, ln sec t cot t is undefined when t (x, y) ( 2 ( 2 11. x length 0 ln 2 0 k (k any integer). Then 3 sin (k )) 16. x et 2t, y 2 3 cos (k ), 1 1 (e t e t, so 2t)2 (1 e t 2 3, 1). The points are (1, 1) and ( 5, 1). 1 cos t, so (1 cos t)2 dt Length 1 ) dt , which using NINT evaluates to sin t, y ( sin t)2 2(1 0 4.497. 17. x Area sin t, y 2 cos t, so sin t) ( sin t)2 sin t) dt 2 cos t) dt t dt 2 2 (2 0 2 cos2 t dt 4 cos2 0 2 0 (2 2t 1 t 2 cos t 0 8 2 t 2 cos dt 2 0 t 2 2 sin 4 2 0 18. x Area t, y 2 , so ( 1 dt 1)3/2 1) 2 0 2 0 12. x Length 2t 3 3, y ( 0 3 1 2t 2) dt t, so 3)2 1 2 t 2 2 3/2 t 3 2 0 t)2 1 2 t dt (1 2t t)2 dt 3 0 4 3 t t2 (t 0 21 2 4 1 2 (t 3 3 4 (5 5 9 14.214 19. x Area 1, y 3 0 2t, so 2 (t 1) 1 (2t)2 dt, 178.561. which using NINT evaluates to ...
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