Solução_Calculo_Stewart_6e

F.
TX.10
CHAPTER 4 REVIEW ¤ 215
7. (a) See l’Hospital’s Rule and the three notes that follow it in Section 4.4.
(b) Write fg as
f
1/g or g
1/f .
(c) Convert the difference into a quotient using a common denominator, rationalizing, factoring, or some other method.
(d) Convert the power to a product by taking the natural logarithm of both sides of y = f g or by writing f g as e g ln f .
8. Without calculus you could get misleading graphs that fail to show the most interesting features of a function.
See the discussion at the beginning of Section 4.5 and the first paragraph in Section 4.6.
9. (a)SeeFigure3inSection4.8.
(b) x 2 = x 1 − f(x 1)
f 0 (x 1 )
(c) x n+1 = x n − f(xn)
f 0 (x n)
(d)Newton’smethodislikelytofailortoworkveryslowlywhenf 0 (x 1) is close to 0. It also fails when f 0 (x i) is undefined,
such as with f(x) =1/x − 2 and x 1 =1.
10. (a) See the definition at the beginning of Section 4.9.
(b) If F 1 and F 2 are both antiderivatives of f on an interval I,thentheydifferbyaconstant.
1. False. For example, take f(x) =x 3 ,thenf 0 (x) =3x 2 and f 0 (0) = 0,butf(0) = 0 is not a maximum or minimum;
(0, 0) is an inflection point.
3. False. For example, f(x) =x is continuous on (0, 1) but attains neither a maximum nor a minimum value on (0, 1).
Don’t confuse this with f being continuous on the closed interval [a, b], which would make the statement true.
5. True. This is an example of part (b) of the I/D Test.
7. False. f 0 (x) =g 0 (x) ⇒ f(x) =g(x)+C. Forexample,iff(x) =x +2and g(x) =x +1,thenf 0 (x) =g 0 (x) =1,
but f(x) 6=g(x).
9. True. The graph of one such function is sketched.
11. True. Let x 1