Pre-Calc Homework Solutions 90

Pre-Calc Homework Solutions 90 - 90 Section 3.5 d tan x dx...

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Unformatted text preview: 90 Section 3.5 d tan x dx d (2x) dx 20. y (x) y (x) sec 2 x sec x cos x On sec 2 x 2 (b) 2 csc x cot x 2 cos x sin2 x 1 ( sin2 x y (x) csc x 1 sin2 x 2 0 0 0 0 1 2 3 at point Q 4 3 cot 4 2 2 1 2 2 2 2 cos x 1) cos x , , the solutions are x 4 4 . The points on the y 3 4 x 1 1 2 The coordinates of Q are 2 csc 3 4 curve are 21. y (x) d (4 dx , 1 and cot x 4 ,1 . 2( 2) ( 1) 2 csc x) 2 csc x cot x 0 csc x csc 2 x 2 2 csc x cot x 2 csc cot 1 1 and passes through 1 x 2 3 ,2 . 4 The equation of the horizontal line is y 2 2. (a) y 2 csc 2 12 2 2 2(1)(0) The tangent line has slope P y (b) csc 2 x 2 23. (a) Velocity: s (t) 2 cos t m/sec Speed: s (t) 2 cos t m/sec Acceleration: s (t) 2 sin t m/sec 2 Jerk: s (t) 2 cos t m/sec 3 (b) Velocity: Speed: 2 cos 2 4 , 2 . Its equation is y x 2 2, or 2 m/sec 2 m/sec 4 2. y (x) 2 csc x cot x 1 sin2 x 2 cos x sin2 x 0 0 0 0 1 2 3 Acceleration: 2 sin Jerk: 2 cos 4 2 m/sec 2 2 m/sec 3 1 (2 cos x sin2 x (c) The body starts at 2, goes to 0 and then oscillates between 0 and 4. Speed: Greatest when cos t at point Q the interval of motion. Zero when cos t 0 (or t k , k odd), at the 2 1) cos x x 1 (or t k ), at the center of y 3 4 4 4 cot 1 3 3 3 2 csc 2 4 2 3 3 endpoints of the interval of motion. 3 3 3 Acceleration: ,4 3 . 4 3. Greatest (in magnitude) when sin t (or t k , k odd) 2 The coordinates of Q are 1 The equation of the horizontal line is y 22. y (x) d (1 dx 2 csc x cot x) ( csc 2 x) Zero when sin t Jerk: 0 (or t k ) 0 2( csc x cot x) 2 csc x cot x csc 2 x cot csc 2 2)2 Greatest (in magnitude) when cos t Zero when cos t 0 or t k , k odd 2 1 (or t k ) (a) y 4 2 csc 4 4 4 2( 2)(1) 2 2 4 ( 24. (a) Velocity: s (t) cos t sin t m/sec Speed: s (t) cos t sin t m/sec Acceleration: s (t) sin t cos t m/sec2 Jerk: s (t) cos t sin t m/sec3 The tangent line has slope P y 4 4 and passes through 4 x 4 , 4 . Its equation is y 4x 4. 4, or ...
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