575 Answers Chapter 4

Selected answers are given here. For a full set of worked solutions, see Specialist Maths Dimensions Units 3 & 4 Solutions and Study Guide.g– 3 h4 --x – 3/2 15+ -----x – 5/24324x --x – 3/2 2+ – --x – 4/34 911 a iyik– 2 3 --x – 4/3 14+ -----x – 3/556x 4 – --x – 5/2 l 2x – 32– 3j105--------x – 11/4 45– -----x – 13/416 4iiyx2 a9e 3xb– x – 2xc– 25 sin5xbiyd18sec 2 3x tan3x(1, 2)e– 4cos2xf– 2 sin( x 2 )–4x 2 cos( x 2 )xg18( cos 2 3x – sin 2 3x)iiyhsec 2 3x – 9 4 -- ( tan 3x ) –3/ 2 27+ ----- ( tan3x) 1/24(1, 2)i– 3e x ( sin( 3e x ) + 3e x cos( 3e x ))xjk–cosec 2 x4sec2x( sec 2 2x + tan 2 2x)ciy′lm– 3e 3 cos x ( cos x – 3sin 2 x)1--x – 1 x 1/ 2 1– cos + --x – 3/2 sin x 1/244–13xno2x – 3 sec 2 x – 1 + 2x – 4 sec 2 x – 1 tan x – 13--x – 5/2 x – 1/2 1cos – --x – 3 sin x – 1/244iiy″3 ab2 cos x – xsinx( 6x – 4x 3 ) cos2x – 12x 2 sin2x1xce x ( 2 + x)diyde – 2x ( 6x – 12x 2 + 4x 3 )ee x log 2x + 2x – 1 – x–2e(1, 0) (7, 0)xfg1sin3x⎛–--x – 3/2 –49 x⎝1/2 ⎞ + 3x⎠–1/ 2 cos3x2e x cos xiiyhe – 2x ( 12 sin 3x – 5 cos 3x )i e – x ( tan x + 2sec 2 xtanx – 2sec 2 x)8 m = 4, 39 k = –3, 3(4, 0)x579Answers