Livro

F.
TX.10

Solução detalhada de todos os exercícios ímpares do livro: Cálculo, James Stewart - VOLUME I e VOLUME II

"O que sabemos é uma gota, o que ignoramos é um oceano." Isaac Newton
23/11/2010.TX

F.
TX.10

1

FUNCTIONS AND MODELS

1.1 Four Ways to Represent a Function
In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here.
1. (a) The point (−1, −2) is on the graph of f , so f (−1) = −2.

(b) When x = 2, y is about 2.8, so f (2) ≈ 2.8.
(c) f (x) = 2 is equivalent to y = 2. When y = 2, we have x = −3 and x = 1.
(d) Reasonable estimates for x when y = 0 are x = −2.5 and x = 0.3.
(e) The domain of f consists of all x-values on the graph of f . For this function, the domain is −3 ≤ x ≤ 3, or [−3, 3].
The range of f consists of all y -values on the graph of f . For this function, the range is −2 ≤ y ≤ 3, or [−2, 3].

(f ) As x increases from −1 to 3, y increases from −2 to 3. Thus, f is increasing on the interval [−1, 3].
3. From Figure 1 in the text, the lowest point occurs at about (t, a) = (12, −85). The highest point occurs at about (17, 115).

Thus, the range of the vertical ground acceleration is −85 ≤ a ≤ 115. Written in interval notation, we get [−85, 115].

5. No, the curve is not the graph of a function because a vertical line intersects the curve more than once. Hence, the curve fails

the Vertical Line Test.
7. Yes, the curve is the graph of a function because it passes the Vertical Line Test. The domain is [−3, 2] and the range

is [−3, −2) ∪ [−1, 3].

9. The person’s weight increased to about 160 pounds at age 20 and stayed fairly steady for 10 years. The person’s weight

dropped to about 120 pounds for the next 5 years, then increased rapidly to about 170 pounds. The next 30 years saw a gradual increase to 190 pounds. Possible reasons for the drop in weight at 30 years of age: diet, exercise, health problems.
11. The water will cool down almost to