Solve the problem.
136)
How much should be deposited semiannually into a sinking fund over 5 years to accumulate
$104,000 if the money earns 8% compounded semiannually?
136)
A)
$17,727.84
B)
$8662.26
C)
$6243.12
D)
$9071.92
Find the monthly house payment necessary to amortize the loan. Assume that interest is compounded monthly.
137)
$254,835 at 8.12% for 25 years
137)
A)
$11,114.26
B)
$1724.38
C)
$2835.49
D)
$1987.16
Solve the problem.
138)
As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework
assignment as she took to complete the preceeding assignment. If it took her 60 minutes to
complete her first assignment, find how long it took her to complete the fifth assignment. Find the
total time she took to complete her first five homework assignments. Round to the nearest minute.
138)
A)
39 min; 246 min
B)
35 min; 206 min
C)
35 min; 246 min
D)
39 min; 206 min
139)
Use the first five terms of the Taylor series to approximate the area of the region bounded by the
standard normal curve, x = 0, x =2.8, and the x–axis. The equation of the standard normal curve is
f(x) =1
e–x2/2.
139)
A)
4.562412
B)
2.489069
C)
1.820139
D)
0.992995
Use l’Hospital’s rule, if applicable, to find the limit.
140)
lim
x
0
1
x+1
6x
140)
A)
0
B)
1
6
C)
–1
D)
Does not exist
Find the common ratio for the geometric sequence.
141)
3, 3
2,3
4,3
8,3
16 ,…
141)
A)
r =1
2
B)
r = 1
C)
r = 3
D)
r =2
Use l’Hospital’s rule, if applicable, to find the limit.
142)
lim
x
2
x2+5–3
x2–4
142)
A)
1
4
B)
1
6
C)
1
3
D)
Does not exist
Find the Taylor series for the given function. Give the interval of convergence.
143)
f(x) = ln(1 +8x)
143)
A)
8x –82
2! x2+83
3! x3–84
4! x4+ . . . +(–1)n8n+1
(n + 1)! xn+1+ . . . ; –1
8, 1
8
B)
8x –82
2x2+83
3x3–84
4x4+ . . . +(–1)n8n+1
n + 1 xn+1+ . . . ; –1
8, 1
8
C)
8x –82
2x2+83
3x3–84
4x4+ . . . +(–1)n8n+1
n + 1 xn+1+ . . . ; (–8, 8)
D)
–8x –82
2! x2+83
3! x3–84
4! x4+ . . . +(–1)n8n
(n + 1)! xn+ . . . ; (–8, 8)
Solve the problem.
144)
After being struck with a hammer, a gong vibrates 48 vibrations in the first second and in each
second thereafter makes 4
5 as many vibrations as in the previous second. Find how many
vibrations the gong makes before it stops vibrating.
144)
A)
55 vibrations
B)
240 vibrations
C)
60 vibrations
D)
250 vibrations
Use l’Hospital’s rule, if applicable, to find the limit.
145)
lim
x
ex
x6
145)
A)
0
B)
1
6
C)
D)
1
720
Find an for the given geometric sequence.
146)
a1=8, r =1
5
146)
A)
an=1
5(8)n
B)
an=81
5
n
C)
an=1
5(8)n–1
D)
an=81
5
n–1
Find the monthly house payment necessary to amortize the loan. Assume that interest is compounded monthly.
147)
$326,248 at 7.79% for 30 years
147)
A)
$3568.47
B)
$2117.89
C)
$12,003.38
D)
$2346.31
Solve the problem.
148)
The population of a small town in 1988 was 10,000 people. Due to decline in industrial growth the
population has since been decreasing at a rate of 2% every year. What was the population of this
town at the end of 1998?
148)
A)
6648
B)
9044
C)
8171
D)
7374
Find the periodic payment that will amount to the given sum under the given conditions. Round to the nearest cent.
149)
S =$29,000; interest is 8% compounded annually; payments are made at the end of each year for 12
years.
149)
A)
$2357.78
B)
$1742.21
C)
$1528.16
D)
$2726.43
Find the amount of the ordinary annuity. Round to the nearest cent.
150)
R =$4300, 8% interest compounded quarterly for 10 years
150)
A)
$259,728.53
B)
$250,420.13
C)
$474,728.53
D)
$62,292.22
Use Newton’s method to find the given root to the nearest thousandth.
151)
345
151)
A)
3.554
B)
3.557
C)
3.551
D)
3.549
Use l’Hospital’s rule, if applicable, to find the limit.
152)
lim
x
0+
x3(ln x)3
152)
A)
0
B)
–1
3
C)
3
D)
Does not exist
Solve the problem.
153)
Green Thumb Landscaping wants to build a $101,000 greenhouse in 2 years. The company sets up a
sinking fund with payments made quarterly. Find the payment into this fund if the money earns
12% compounded quarterly.
153)
A)
$11,358.10
B)
$7116.46
C)
$9941.43
D)
$5322.70
Use the appropriate Taylor polynomial of degree 3 at x = 0 to approximate the quantity. Round the answer to four
decimal places.
154)
4.8
154)
A)
2.1900
B)
2.0365
C)
1.7536
D)
2.2100
Use l’Hospital’s rule, if applicable, to find the limit.
155)
lim
x
1
x–x2
ln x
155)
A)
–3
2
B)
0
C)
–1
D)
–2
Find the amount of the ordinary annuity. Round to the nearest cent.
156)
R =$560, i =0.05, n =13 (Interest is compounded annually.)
156)
A)
$8913.59
B)
$21,119.27
C)
$9919.27
D)
$2011.36
The nth term of a sequence is given. Calculate the fifth partial sum.
157)
an=(–1)n+(–1)2n
(5n + 1)(5n + 2)
157)
A)
3
154
B)
2
231
C)
1
63
D)
17
1386
Solve the problem.
158)
In a certain country, the infant mortality rate is 6.7 per 1000 live births. Assuming that this is the
expected value for a Poisson distribution, find the probability that in a random sample of 1000 live
births, there were fewer than 5 cases of infant mortality.
158)
A)
0.202159
B)
0.242591
C)
0.173279
D)
0.161727
Find an for the given geometric sequence.
159)
1
3, 1
6, 1
12 , 1
24 , . . .
159)
A)
an=1
3
1
2
n
B)
an=1
3+1
2(n – 1)
C)
an=1
3–1
6(n – 1)
D)
an=1
3
1
2
n – 1
The nth term of a sequence is given. Calculate the fifth partial sum.
160)
an=(–1)n
5n – 1
160)
A)
–1909
9576
B)
–7283
114,912
C)
–16,441
229,824
D)
–3397
76,608
Find the sum of the first five terms of the indicated geometric series.
161)
a1=2.95, r =3.817
161)
A)
435.36
B)
221.24
C)
146.29
D)
847.44
Use l’Hospital’s rule, if applicable, to find the limit.
162)
lim
x
0
(3 + x)ln(x + 1)
ex– 1
162)
A)
3
B)
1
3
C)
0
D)
Does not exist
Identify which geometric series converge. Give the sum of a convergent series.
163)
3+15 +75 +375 + . . .
163)
A)
Converges to 3750
B)
Converges to 1875
C)
Converges to 5625
D)
Diverges
Use l’Hospital’s rule, if applicable, to find the limit.
164)
lim
x
0
1 +3x –1 –3x
x
164)
A)
1
B)
1
6
C)
3
D)
1
3
Answer Key
Testname: C12
Answer Key
Testname: C12
Answer Key
Testname: C12
Answer Key
Testname: C12
Answer Key
Testname: C12