Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

SECTION 10.2 CALCULUS WITH PARAMETRIC CURVES 0 11
45.
( ~~ ) 2 + ( !fJd = [e'(cos t - sin t)f + [et(sin t +cos t)f
= (e') 2 (cos 2 t - 2 cos t sin t + sin 2 t) '
+ (et) 2 (sin 2 t+2sint cost+cos 2 t
= e 2 t(2 cos 2 t + 2 sin 2 t) = 2e 2 t
Thus, L = J~" .J2e2t dt = f 0
" -12 et dt =·-12 [ e' ]~ = -/2 (e,.- 1).
47.
1. 4 The figure shows the curve x = sin t + sin 1. 5t, y = cost for 0 .:::; t 5 47r.
. dx/dt = cost+ 1.5 cos 1.5t and dy/ dt = -sin t, so
-2.1 f->o.o--------,.£-f->'