REVIEW CHAPTER 1
No Calculator:
1. What is lim
x 
(A)
9x 2  2
?
4x  3
3
2
(B)
2. What is lim
x 
2
3
3
4
(C)
1
2
(C) 1
(D) 1
(E) The limit does not exist.
3
2
(E) The limit does not exist.
(D) 2
(E) The limit does not exist.
x 1
?
x 1
(A) 0
(B)
(D)
x2  6
?
x  2  x  3 x 2
3. What is lim
(B) 
(A) -3
1
3
(C)
1
3
x
x
4. lim is
x 0
(A) 1
5. lim
x 0
(B) 0
(C) ∞
(D) -1
(E) Nonexistent
(B) ½
(C) 2/3
(D) 3/2
(E) ∞
(B) -1
(C) 0
(D) 3
(E) ∞
(B) = 1/5
(C) =1
(D) = 5
(E) Does not exist
(B) 1/3
(C) 3
(D) ∞
(E) ¼
tan 3x
=
2x
(A) 0
5 x 3  27
is
x   20 x 2  10 x  9
6. lim
(A) -∞
7. lim
x 0
sin 5 x
x
(A) =0
8. lim
x 0
(A) 1
sin x
is
x 2  3x
3x 2  4
?
x  2  7 x  x 2
9. What is lim
(A) 3
(B) 1
(C) -3
(D) ∞
(E) 0
(C) 1
(D) 3
(E) The limit does not exist.
(B) 0
(C) 1
(D) 2
(E) the limit does not exist.
(B) -1
(C) 10
(D) 1
(E) 2
(D) -1
(E) None of these
3x 2  1
?
x  (3  x )(3  x )
10. What is lim
(A) -9
(B) -3
 1

 1

?
11. What is lim x  1
x 0 
x





(A) -1
12. lim
x 1
x 2  2x  3

x2 1
(A) -2
|x|
is
x 0 x
13. lim
(A) 0
(B) nonexistent
 x2 1

14. Let f ( x)   x  1
 4

I. lim f ( x)
x 1
if
(C) 1
x 1
Which of the following statements is (are) true?
if
x 1
exist
II. f(1) exists
III. f is continuous at x=1
(A) I only
(B) II only
(C) I and II only (D) None
(E) I, II and III
15. What is lim x x ?
x 0
(A) = 0
(B) = 1
(C) = e
(D) = ∞
(E) Does not exist.
16. The function f is continuous at x =1 .
 x  3  3x  1

x 1
If f ( x)  

k

(A) 0
for
x 1
then k=
for
(B) 1
x 1
(C)
1
2
17. Which statement is true about the curve y 
(D) 
1
2
(E) none of the above
2x 2  4
?
2  7 x  4x 2
(A) The line x = -1/4 is a vertical asymptote
(B) The line x = 1 is a vertical asymptote
(C) The line y = -1/4 is a horizontal asymptote
(D) The graph has no vertical or horizontal asymptote
(E) The line y = 2 is a horizontal asymptote
18. Which of the following is true about the function f if f ( x) 
( x  1) 2
?
2 x 2  5x  3
I. f is continuous at x = 1.
II. The graph of f has a vertical asymptote at x = 1.
III. The graph of f has a horizontal asymptote at y =
(A) I only
(B) II only
1
.
2
(C) III only
(D) II and III only
(E) I, II, and III
(C) I and II only
(D) II and III only
(E) I, II, III
(C) -5
(D) -1
(E) 3
19. Which of the following is continuous at x = 1?
I. f(x) = |x – 1|
II. f(x) = ex-1
III. f(x) = ln(ex-1 – 1)
(A) I only
(B) II only
20. If f(x) = x3 – 2x – 1, then f(-2) =
(A) -17
(B) -13
21. The domain of
(A) all x≠0,1
x2
is
x x
2
(B) x ≤2, x≠0,1 (C) x≤2
(D) x≥2
(E) x>2
22. If f(x) = x3 + Ax2 + Bx – 3 and if f(1) = 4 and f(-1) = -6, what is the value of 2A + B?
(A) 12
(B) 8
(C) 0
(D) -2
(E) Cannot be determined
23. Which of the following function is NOT odd?
(A) f ( x)  sin x
(B) f ( x)  sin 2 x (C) f ( x)  x 3  1
(D) f ( x) 
x
x 1
2
(E) f ( x)  3 2 x
24. Which of the following is a reflection of the graph of y = f(x) over the x-axis?
(A) y = -f(x)
(B) y = f(-x)
(C) y = |f(x)|
(D) y = f(|x|)
(E) y = -f(-x)
25. The set of x-intercepts of the graph of f(x) = x3 – 2x2 – x + 2 is
(A) {1}
(B) {-1, 1}
(C) {1,2}
(D) {-1,1,2}
(E) {-1,-2,2}
(D) {2}
(E) {2,-2}
26. The set of zeros of f(x) = x3 + 4x2 + 4x is
(A) {-2}
(B) {0,-2}
(C) (0,2}
27. The values of x for which the graphs of y = x + 2 and y2 = 4x intersect are
(A) -2 and 2
(B) -2
(C) 2
(D) 0
(E) None of these
28. Let f(x) have an inverse function g(x). Then f(g(x)) =
(A) 1
(B) x
 2
 3
29. The period of f ( x)  sin 
(A)
1
3
(B)
2
3
(C)
1
x
(D) f(x)∙g(x)
(E) None of these
(C)
3
2
(D) 3
(E) 6

x  is

CALCULATOR SECTION:
30. The function f is defined on the interval [-4,4] and
its graph is shown to the right. Which of the following
statements are true?
I. lim f ( x)  1
x 1
II. lim f ( x)  f (3)
x  1
III. f (2)  0
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III
(D) ∞
(E) Nonexistent
 x 2 / x if x  0

31. The function f ( x)  
 0 if x  0

(A)
(B)
(C)
(D)
(E)
is continuous everywhere
is continuous except at x = 0
has a removable discontinuity at x = 0
has an infinite discontinuity at x=0
has x=0 as a vertical asymptote
32. lim[ x] (where [x] is the greatest integer in x) is
x 2
(A) 1
(B) 2
(C) 3
33 Which function could have the graph shown to the right?
x
x 1
2x
(C) y  2
x 1
4x
(E) y 
x 1
(A) y 
2
4x
x 1
x2  3
(D) y  2
x 1
(B) y 
2
34. The graph of a function f is shown to the right.
Which of the following statements about f is false?
(A) lim f ( x)  lim f ( x)
xa
xa
(B) lim f ( x)  f (a )
x a
(C) f(a) > 0
(D) rule 3 fails for continuity
(E) lim f ( x)  f (a)
x a
 x 2  kx  3

35. The function f is defined on all the reals such that f ( x)  
 3x  b

for
x 1
for
x 1
For which of the following values of k and b will the function be continuous on its entire domain?
(A) k=-1, b=-3
36. The graph of y 
(B) k=1, b=3
(C) k=1, b=4
(D) k=1, b=-4
(E) k=-1, b=6
(C) III only
(D) I and III only
(E) II and III only
sin x
has
x
I. a vertical asymptote at x = 0
II. a horizontal asymptote at y = 0
III. an infinite number of zeros
(A) I only
(B) II only
37. For what value(s) of a is it true that lim f ( x ) exists and f(a)
x a
exists, but lim f ( x)  f (a) ? It is possible that a=
x a
(A) -1 only
(C) 2 only
(E) -1 or 2 only
(B) 1 only
(D) -1 and 1 only
38. Which statements about limits at x = 1 are true?
I. lim f ( x)
exists
II. lim f ( x)
exists
III. lim f ( x )
exists
x 1
x 1
x 1
(A) None of I, II, or III
(B) I only
39. A function f(x) equals
(C) II only
(D) I and II only
(E) I, II, and III
x2  x
for all x except x = 1. For the function to be continuous at x = 1, the value of f(1) must
x 1
be
(A) 0
(B) 1
(C) 2
(D) e
(E) ∞