Solução_Calculo_Stewart_6e

F.
TX.10
1.4 Graphing Calculators and Computers
SECTION 1.4 GRAPHING CALCULATORS AND COMPUTERS ¤ 23
1. f(x) = √ x 3 − 5x 2
(a) [−5, 5] by [−5, 5]
(There is no graph shown.)
(b) [0, 10] by [0, 2] (c) [0, 10] by [0, 10]
The most appropriate graph is produced in viewing rectangle (c).
3. Since the graph of f(x) =5+20x − x 2 is a
parabola opening downward, an appropriate viewing
rectangle should include the maximum point.
5. f(x) = 4√ 81 − x 4 is defined when 81 − x 4 ≥ 0 ⇔
x 4 ≤ 81 ⇔ |x| ≤ 3, so the domain of f is [−3, 3]. Also
0 ≤ 4√ 81 − x 4 ≤ 4√ 81 = 3,sotherangeis[0, 3].
7. The graph of f(x) =x 3 − 225x is symmetric with respect to the origin.
Since f(x) =x 3 − 225x = x(x 2 − 225) = x(x + 15)(x − 15),there
are x-intercepts at 0, −15,and15. f(20) = 3500.
9. The period of g(x) = sin(1000x) is 2π ≈ 0.0063 and its range is
1000
[−1, 1]. Sincef(x) =sin 2 (1000x) is the square of g,itsrangeis
[0, 1] and a viewing rectangle of [−0.01, 0.01] by [0, 1.1] seems
appropriate.
11. The domain of y = √ x is x ≥ 0,sothedomainoff(x) =sin √ x is [0, ∞)
and the range is [−1, 1]. With a little trial-and-error experimentation, we find
that an Xmax of 100 illustrates the general shape of f,soanappropriate
viewing rectangle is [0, 100] by [−1.5, 1.5].