NAME
AUGUST 30, 2013
AB CALCULUS UNIT I QUIZ
LIMITS and CONTINUITY
I.
MULTIPLE CHOICE: Non-calculator. Please show all work on a separate sheet of
paper for partial credit.
1.
f(x) is a continuous function and f(1) = 2, f(3) = 4. Which of the following values
must f(x) necessarily attain on the domain (1,3)?
I.
3/2
a) I only
2.
II.
b) II only
b) 0
a) 1
4.
III.
3
c) II and III only d) I, II, and III
e) none of these
c) 1
d) 2
e) does not exist
c) 3
d) 
e)
 1

 x -1 +1 
What is lim 
 ?
x 0
x




a) -1
3.
5/2
sinx
is
2
x  0 x + 3x
1
b)
3
lim
1
4
x2 - x + 5, x < 2

x =2
Suppose that h(x) 5,
x3 -1,
x>2

Which of the following is equal to 7?
I.
lim h(x)
II.
x2-
a) I only
5.
b) II only
lim h(x)
x2+
c) III only
III.
limh(x)
x 2
d) I and II only
e) I, II, and III
The graphs of y  x and y  3 x  2  1 are related. Of reflection, stretching,
shrinking, vertical translation and horizontal translation, which should be done first?
a) reflection
b) stretching
c) vertical translation
d) horizontal translation
e) shrinking
6.
Let
 x2 -1
if x  1

f(x) =  x -1
 4 if x = 1

Which of the following statements, I, II, or III, are true?
I. limf (x ) exists
x 1
a) only I
7.
II. f(1) exists
b) only II
c) I and II
xa
and
Which of the following statements is/are true?
1
a) lim 4f(x) × g(x) = 24
b) lim f (x )  4
x a
x a 2
f(x) + g(x) 7
d) lim
=x a
g(x)
3
a)
d) none of them
e) all of them
f(x) and g(x) are defined for all x and
lim f(x) = 8
8.
negative?
III. f is continuous at x=1
lim g(x) = -6
xa
c) lim f(x) - g(x) =14
xa
2 - g(x)
=1
x  a f(x)
e) lim
For which of the given angles, if any, is the sin and tan positive and the cos

b)
3
2
3
c)
4
3
d)
5
3
9.
[-7,7] x [-5,5]
Which of the following statements is/are true for the function y  f (x ).
a) f ( 1)  1; lim f (x )  1; f(x) is continuous at x = -1.
x 1
b) f ( 4)  2; lim f (x )  2; f(x) is continuous at x = -4.
x 4
c) f (2)  3; lim f (x )  1; f(x) is continuous at x = 2.
x 2
d) f (5)  1; lim f (x ) does not exist; f(x) is not continuous at x = 5.
x 5
e) None of these is true.
e) no angle exists
NAME
AUGUST 30, 2013
AB CALCULUS UNIT I QUIZ
LIMITS and CONTINUITY
I.
PROBLEMS: Non-calculator. Please show all work below.
1.
The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the
limit does not exist, explain why.
g(x)
f(x)
[-3,3] x [-2,3]
[-3,3] x [-2,3]
a)
lim f(x) + g(x)
b)
limf(x) + g(x)
c)
lim f(x) × g(x)
d)
f(x)
x -1 g(x)
e)
limx3f(x)
f)
lim f (x )
h)
g)
x2
x0
x2
x-3+
x1
lim
lim 3 + f(x)
x -1
lim f (x )
x 3
I pledge that the work on this paper is my own and I abided by the directions given.
I also pledge that I will NOT discuss the contents of this evaluation with anyone else
until it is graded and returned to me.
over
2.
 x  1, x  2

 x  1,  2  x  1

Let g ( x )   x  3, 1  x  6
 6
8x, 6  x 7

 6, 7  x  10
a) Graph g(x) below making sure you carefully draw open and closed circles where
appropriate. Please try to represent curves as such and not as straight lines!
[-10,10] x [-10,10]
b) Identify the domain and range of g(x).
D:
R:
For the next six questions, if your answer is no, explain why.
c) Determine if g(x) is continuous from the right at x = -2.
d) Does lim g ( x ) exist? Justify your answer.
x 1
e) Determine if g(x) is continuous from the left at x = 1.
f) Determine if g(x) is continuous at x = 7.
g) Does lim g ( x ) exist? Justify your answer.
x 2
h) Determine if g is continuous at x = 9.