Page 159 - Calculus Demystified

CHAPTER 5
146
(c) lim ln[x/(x + 1)]· (x + 1) Indeterminate Forms
x→+∞
(d) lim ln x · e −x
x→+∞
(e) lim e 2x · x 2
x→−∞
(f) lim x · e 1/x
x→0
4. Evaluate each of the following improper integrals. In each case, be sure to
write the integral as an appropriate limit.
1
(a) x −3/4 dx
0
3

(b) (x − 3) −4/3 dx
1

2 1
(c) dx
−2 (x + 1) 1/3
6 x
(d) dx
−4 (x − 1)(x + 2)

8 x + 4
(e) dx
4 (x − 8) 1/3
3 sin x

(f) 2 dx
0 x
5. Evaluate each of the following improper integrals. In each case, be sure to
write the integral as an appropriate limit.

∞
(a) e −3x dx
1

∞
2 −x
(b) x e dx
2

∞
(c) x ln xdx
0

∞ dx
(d) 2
1 1 + x

∞ dx
(e)
1 x
−1 dx

(f)
2
−∞ x + x