Solução_Calculo_Stewart_6e

F.
TX.10
SECTION 2.6 LIMITS AT INFINITY; HORIZONTAL ASYMPTOTES ¤ 65
(b) From part (a), the horizontal asymptote is y =0. The function
y =(sinx)/x crosses the horizontal asymptote whenever sin x =0;
that is, at x = πn for every integer n. Thus, the graph crosses the
asymptote an infinite number of times.
55. Divide the numerator and the denominator by the highest power of x in Q(x).
(a) If deg Pdeg Q, then the numerator → ±∞ but the denominator doesn’t, so lim [P (x)/Q(x)] = ±∞
x→∞
57. lim
x→∞
(depending on the ratio of the leading coefficients of P and Q).
5 √ x
√ · 1/√ x
x − 1 1/ √ x = lim
x→∞
5
1 − (1/x)
=
5
√ 1 − 0
=5and
10e x − 21
lim
· 1/ex
x→∞ 2e x 1/e = lim 10 − (21/e x )
= 10 − 0 =5.Since 10ex − 21