Solução_Calculo_Stewart_6e

F.
TX.10
24 ¤ CHAPTER 1 FUNCTIONS AND MODELS
13. The first term, 10 sin x, has period 2π and range [−10, 10]. It will be the dominant term in any “large” graph of
y =10sinx +sin100x, as shown in the first figure. The second term, sin 100x,hasperiod 2π = π and range [−1, 1].
100 50
Itcausesthebumpsinthefirst figure and will be the dominant term in any “small” graph, as shown in the view near the
origin in the second figure.
15. We must solve the given equation for y to obtain equations for the upper and
lower halves of the ellipse.
4x 2 +2y 2 =1 ⇔ 2y 2 =1− 4x 2 ⇔ y 2 = 1 − 4x2
2
1 − 4x
2
y = ±
2
⇔
17. From the graph of y =3x 2 − 6x +1
and y =0.23x − 2.25 in the viewing
rectangle [−1, 3] by [−2.5, 1.5],itis
difficult to see if the graphs intersect.
If we zoom in on the fourth quadrant,
we see the graphs do not intersect.
19. From the graph of f(x) =x 3 − 9x 2 − 4, we see that there is one solution
of the equation f(x) =0and it is slightly larger than 9. By zooming in or
using a root or zero feature, we obtain x ≈ 9.05.
21. We see that the graphs of f(x) =x 2 and g(x) =sinx intersect twice. One
solution is x =0. The other solution of f = g is the x-coordinate of the
point of intersection in the first quadrant. Using an intersect feature or
zooming in, we find this value to be approximately 0.88. Alternatively, we
could find that value by finding the positive zero of h(x) =x 2 − sin x.
Note: After producing the graph on a TI-83 Plus, we can find the approximate value 0.88 by using the following keystrokes:
. The “1” is just a guess for 0.88.