Name: ________________________
Class: ___________________
Date: __________
MAT 210 Test 1 Review for Final
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Estimate the limit numerically.
2
x
lim
x→0 x + 2
a.
b.
c.
d.
e.
-2
0
diverges to +∞
1
diverges to - ∞
2. Use the graph to compute the given quantity.
lim f(x)
x→ 2
a.
b.
c.
d.
e.
+∞
28
1
0
-∞
1
ID: A
Name: ________________________
ID: A
4. The graph of a function f is given. Determine
whether f is continuous on its domain.
3. Use the graph to compute lim f(x) and lim f(x).
x→0 −
x→0 +
a.
b.
a.
b.
lim f(x) = 7, lim f(x) = −1.
x→0 −
x→0 +
Discontinuous
Continuous
5. The graph of a function f is given. Determine
whether f is continuous on its domain.
lim f(x) = −1, lim f(x) = −1.
x→0 −
x→0 +
c.
lim f(x) = 7, lim f(x) = 7.
x→0 −
x→0 +
d. + ∞
e. does not exist
a.
b.
2
Continuous
Discontinuous
Name: ________________________
ID: A
6. Determine what, if any, value to assign to f(a) to
make f continuous at x = a.
f(x) =
a.
b.
c.
d.
e.
1−e
x
x
9. Calculate the limit algebraically.
2
6h
lim
h → 0 h + 7h 2
; a=0
a.
b.
c.
f(0) = 1
f(0) = 3
f(0) = -1
f(0) = -3
No value of f(0) will make it continuous at 0.
d.
e.
7. Use a graph to determine whether the function is
continuous on its domain. If it is not continuous
on its domain, list the points of discontinuity.
ÔÏÔ
ÔÔ
Ô 7x + 2
g(x) = ÔÌÔ
ÔÔ
ÔÔ 6x + 2
ÔÓ
a.
b.
c.
d.
e.
The
The
The
The
The
10. Calculate the limit algebraically.
7x
lim
x → +∞
if x < 0
if x ≥ 0
a.
point of discontinuity: 2.
function is continuous on its domain.
points of discontinuity: -2, 0.
point of discontinuity: 0.
points of discontinuity: 2, 0.
b.
c.
d.
e.
8. Calculate the limit algebraically.
6+x
lim
x→5 x
a.
b.
c.
d.
e.
-0.857
6
-6
6
7
0
6
2.2
1.2
11
–5
3
6
7
12
1
12
12
7
−
12
11
12
3
+ 10000x + 10000000
6
3
12x + 8000x
Name: ________________________
ID: A
È
˘
11. Calculate the average rate of change of the given function over the interval ÍÍÎ 2, 2.25 ˙˙˚ .
p($)
q(p) (items)
a.
b.
c.
d.
e.
2
600
2.25
400
2.5
250
4,000
800
–50
–200
–800
12. Calculate the average rate of change of the given
function (Inflation (%) of Budget deficit (% of
È
˘
GNP)) over the interval ÍÍÎ 0, 2 ˙˙˚ .
3
14. The function R(t) = 120 + 8t represents the
value of the U.S. dollar in Indian rupees as a
function of time t in days. Estimate (using h =
0.0001) the instantaneous rate of change of R at
time t = 5.
Please select the correct answer rounded to the
nearest whole number.
a.
b.
c.
d.
e.
603
600
605
602
596
15. Estimate the slope of the tangent to the graph of
the following function at the point x = -3.
a.
b.
c.
d.
e.
f(x) = x
1
–0.5
8
5
–20
a.
b.
c.
d.
e.
13. Calculate the average rate of change of the given
È
˘
function over the interval ÍÍÎ -10, 0 ˙˙˚ .
f( x ) = 4x + 4
a.
b.
c.
d.
e.
4
–44
40
–4
–40
4
2
18
11
–6
6
–11
Name: ________________________
ID: A
16. Find an equation of the tangent line to the graph
1
of the function f(x) = x +
at the point that has
x
1
x-coordinate x = .
4
a.
b.
c.
d.
e.
20. Find the derivative of the function.
g (x) = 5x
y = 15x + 8
y = -15x + 8
y = -15x -120
y = 8x − 15
y = x -15
a.
b.
c.
d.
e.
−7
−3
−6
g'(x) = -15x
− 36x
−3
−6
g'(x) = 5x
+ 6x
−4
−7
g'(x) = -5x
− 6x
−4
−7
g'(x) = 15x
+ 36x
s(x) = 2
1
ln 4
1
4
ln 4
–50
–45
–49
–46
–48
-18x
-72
72
-36
48
− 36x
21. Find the derivative of the function.
39
x +
a.
s'(x) =
b.
s'(x) =
c.
s'(x) =
d.
s'(x) =
e.
s'(x) =
x
2
x
1
x
1
x
1
x
1
x
−
−
+
+
+
39
x x
19.5
x x
19.5
x
x
39
x x
19.5
x
x
22. Find the slope of the tangent to the graph of the
3
given function f(x) = 2x at the point (-3, -54).
19. Compute f '(a) for a = 2.
a.
b.
c.
d.
e.
−4
b.
e.
0
f(x) = 2 − 6 x
−6
g'(x) = -15x
d.
18. If a stone is dropped from a height of 404 feet,
its height after t seconds is given by
2
S = 404 − 8t . Find the stone's average velocity
over the period [2, 4].
a.
b.
c.
d.
e.
+ 6x
a.
c.
17. Estimate f '(4) of the function f = 4 ln(x).
−3
3
a.
b.
c.
d.
e.
2
5
f '(-3)
f '(-3)
f '(-3)
f '(-3)
f '(-3)
= 18
= -18
= -162
= 54
=0
Name: ________________________
ID: A
23. Find all the values of x (if any) where the tangent
line to the graph of the given equation is
horizontal.
y = 4x
a.
b.
c.
d.
e.
2
+ 13x + 13
x = -6.5
x = 6.5
x = -1.63
x=0
x = 1.63
24. Given.
lim
x→7
x
2
− 14x + 49
2
x − 7x
Say whether L'Hospital's rule applies. It is does,
use it to evaluate the given limit. If not, use some
other method.
a.
b.
c.
d.
e.
yes, 7
no, 7
yes, 5
no, 0
yes, 0
25. Given.
2
x + 14x + 24
lim
x → −2 x 2 + 2x
Say whether L'Hospital's rule applies. It is does,
use it to evaluate the given limit. If not, use some
other method.
a.
b.
c.
d.
e.
no, -12
yes, 12
no, -5
yes, -5
no, 5
6
ID: A
MAT 210 Test 1 Review for Final
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
D
A
B
B
C
B
B
E
A
E
A
A
B
C
B
C
E
B
A
B
D
C
E
D
PTS:
PTS:
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PTS:
PTS:
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PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
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PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1