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

SECTION 10.1 CURVES DEFINED BY PARAMETRIC EQUATIONS D 3
25. When t = - 1,-(x,y) = (0, - 1). As t increases to 0, x decreases to - 1 andy
increases to 0. As t increases from 0 to 1, x increases to 0 and y increases. to 1.
As { increases beyo~d 1, both x and y increase. Fort < - 1, x is positive and
decreasing and y is negative and increasing. We could achieve greater accuracy
by estimating x- and y-values for selected values oft from the given graphs and
(-1,0) X
t=O
t=-1
plotting the correspo~ding points.
27. When t = 0 we see that x = 0 and y = 0, so the curve starts at the origin. As t
y
increases from 0 to~. the graphs show that y increases from 0 to 1 while x
increases from 0 to 1, decreases to 0 and to - 1, then increas.es back to 0, so we
arrive at the point (0, 1). Sinlilarly, as t increases from ~ to 1, y decreases from 1
X
to 0 while x repeats its pattern, and we arrive back at the origin. We could achieve greater accuracy by estimating x- and
y-values for selected values oft from the given graphs and plotting the corresponding points.
29. Use y = t and x = t - 2sin 7ft with at-interval of [-7r, 7r].
31. (a) x = X1 + (x2 - x1)t, y = YI + (y2- Y1)t, 0 5 t 5 1. Clearly the curve passes through P1(X1, Yl) when t = 0 and
through P2(x2, y2) when t = 1. For 0