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Pre-Calc Homework Solutions 91

# Pre-Calc Homework Solutions 91 - Section 3.5 cos(x h cos x...

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Unformatted text preview: Section 3.5 cos (x h) cos x d cos x lim h dx h0 cos x cos h sin x sin h cos x lim h h0 (cos x)(cos h 1) sin x sin h lim h h0 h0 91 (b) Velocity: cos Speed: 0 4 sin 4 0 m/sec (d) 0 m/sec sin sin 4 4 Acceleration: Jerk: cos 4 cos 4 2 m/sec2 0 m/sec3 2 and then oscillates (c) The body starts at 1, goes to between 2. Speed: Greatest when t Zero when t Acceleration: Greatest (in magnitude) when t Zero when t Jerk: Greatest (in magnitude) when t Zero when t 25. (a) 4 3 4 4 3 4 lim cos x h0 lim cos h h 180 1 h0 lim sin x h0 lim sin h h (cos x)(0) 180 (sin x) sin x d cos x dx 180 k (e) k d2 sin x dx 2 2 180 180 sin x 1802 4 sin x d dx 2 2 2 k d sin x dx 3 3 3 180 sin x 1802 180 cos x k 2 1803 3 4 cos x d dx 180 k d cos x dx 2 2 sin x 180 180 cos x k 1802 d cos x dx 3 3 3 cos x d dx 2 2 2 180 cos x 1802 180 sin x 1803 sin x 26. y [ 360, 360] by [ 0.01, 0.02] y The limit is 180 because this is the conversion factor d csc x csc x cot x dx d ( csc x cot x) dx d d (csc x) (cot x) (cot x) (csc x) dx dx for changing from degrees to radians. (b) (csc x)( csc2 x) csc3 x 27. y csc x cot2 x (cot x)( csc x cot x) [ 360, 360] by [ 0.02, 0.02] d ( tan ) d d (tan ) d (tan ) tan d ( ) d This limit is still 0. (c) d sin x dx sec2 y h) sin x h sin x cos h cos x sin h sin x lim h h0 sin x(cos h 1) cos x sin h lim h h0 cos h 1 lim sin x lim lim cos x h h0 h0 h0 h0 lim sin (x d ( sec2 tan ) d d d d [(sec )(sec )] (sec2 ) ( ) (tan ) d d d d d (sec ) (sec ) (sec ) (sec ) sec2 d d sin h h0 h lim sec2 2 sec2 (2 tan tan 2 sec2 (sin x)(0) 180 (cos x) 180 2)(sec2 ) cos x or, writing in terms of sines and cosines, 2 2 tan cos2 2 cos 2 sin cos3 ...
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