Pre-Calc Homework Solutions 90

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online