VU Calculus
Unit 1 Review
No Calculators
Name: ______________________________________
I. The graph of a function f is shown below.
6
f
4
2
-10
-5
5
10
-2
-4
Answer the following questions about function f.
1) f (5) 
2) f (2) 
3) f (4) 
4) lim f ( x) 
5) lim f ( x) 
6) lim f ( x) 
7) lim f ( x) 
8) lim f ( x) 
9) lim f ( x) 
10) lim f ( x) 
11) lim f ( x) 
12) lim f ( x) 
x 7
x4
x  0
x 5
x 0
x  4
x2
x  0
x  4
13) Use the definition of a continuous function at a number to answer the following.
a. f is not continuous at x = -7 because:_____________________________________________________
b. f is not continuous at x = 2 because:______________________________________________________
c. f is not continuous at x = 4 because:______________________________________________________
No Calculators
14) lim
x→2
-x2 + 4x
a) 0
15) lim
x 9
a)
x →0
c) 4
d) -12
b) does not exist
c) 3
d)
e) None of these
x 3
x9
1
3
16) lim
b) 12
1
6
x
tan x
17) lim sinx
x →1
18)
True or False: If f is undefined at x = c, then the limit of f(x) as x approaches c does not exist.
19)
True of False: If the lim f(x)  L then f(c) = L.
xc
e) None of these
20)
2

 x  3x  6 when x  2
Find lim f(x) when f(x) =  2
x →2

 x  3x  2 when x  2
21)
Find a c such that f(x) is continuous on the entire real line.
x 2 when x  4

f(x) =  c
when
x 4

x
22)
Find the x-values (if any) at which f is discontinuous. Label as removable or non-removable.
f(x) =
a)
b)
c)
d)
e)
2x  6
2x 2  18
x = 3 only….Non-removable
x = - 3 only…Non-removable
x = 3 and x = -3…Both non-removable
x = -3…Removable, x = 3…Non-removable
There are no discontinuities
23) Determine all of the vertical asymptotes of f(x):
x 2
f(x) = 2
x -4
a)
V.A at x = 2 only
b) V.A. at x = -2 only
c) V.A. at x = -2 and x = 2
d) No V.A’s
e) None of these
24) If a  0, then lim
x  a
a)
x 2 - a2
is:
x 4 - a4
1
6a2
b) 0
c)
1
a2
d)
1
2a2
e) Does not exist
25) If the function f is continuous on the closed interval [0, 2] and has values that are given in the table
below, then the equation f(x) = ½ must have at least TWO solutions in the interval [0, 2] if k = ? Hint! Draw a picture!
x
f(x)
a)
b)
c)
d)
e)
0
1
1
k
2
2
0
½
1
2
3
26) The graph of the function f is shown to the right.
Which of the following statements is false?
a)
b)
c)
d)
e)
x = a is in the domain of f.
lim f(x)
x a
is equal to
lim f(x) exists
x a
lim
x a
is not equal to
f is continuous at x = a
f(a)
lim f(x)
x a
VU Calculus
Unit 1 Review
Calculators may be used.
Name: _________________________________
1) Decide whether the following problem can be solved using precalculus,
or whether calculus is required. If the problem can be solved using
precalculus, solve it. If the problem seems to require calculus, use a
graphical or numerical approach to estimate the solution.
Find the area of the shaded region.
2) Consider the function f  x  
x and the point P  4, 2  on the graph of f . Graph f and the secant line passing
through P  4, 2  and Q  x, f  x   for x  1 and find its slope.
3)
Approximate the limit numerically by completing the table:
x
f(x)
1.9
4) Find the limit: lim
x0
1.99
1.999
2
lim x = ___________
x 2
2
x -2
2.001
2.01
2.1
(x  x)2  2(x  x)  1  (x 2  2x  1)
x
5) Use a graphing utility to graph the function f  x  
x 2  3x  9
x3  27
and determine the one-sided limit lim f  x  .

x 3