Page 330 - Calculus Demystified

Final Exam
3
(c) f −1 (x) = x − x 317
(d) f −1 (x) = x/(x + 1)
3
(e) f −1 (x) = x − 1
3
a · b −2
21. The expression ln simplifies to
4
c /d −3
(a) 3 ln a − 2ln b − 4ln c + 3ln d
(b) 3 ln a + 2ln b + 4ln c − 3ln d
(c) 4 ln a − 3ln b + 2ln c − 4ln d
(d) 3 ln a − 4ln b + 3ln c − 2ln d
(e) 4 ln a − 2ln b + 2ln c + 2ln d
2
22. The expression e ln a −ln b 3 simplifies to
(a) 2a · 3b
2a
(b)
3b
2
(c) a · b 3
a 2
(d)
b 3
2 3
(e) 6a b

x 2 if x< 1
23. The function f(x) = has limits
x if x ≥ 1
(a) 2 at c = 1 and −1at c = 0
(b) 1 at c = 1and4at c =−2
(c) 0 at c = 0and3at c = 5
(d) −3at c =−3and2at c = 1
(e) 1 at c = 0and2at c = 2
x
24. The function f(x) = has limits
2
x − 1
(a) 3 at c = 1and2at c =−1
(b) ∞ at c = 1and0at c =−1
(c) 0 at c = 0 and nonexistent at c =±1
(d) 2 at c =−2 and −2at c = 2
(e) −∞ at c = 1 and +∞ at c =−1

x 3 if x< 2
25. The function f(x) = √ is continuous at
x if x ≥ 2
(a) x = 2 and x = 3