MA 312 - Section Number _________
Final Exam
Name__________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the integral.
(8x2 + x-3 ) dx
1)
A)
1)
8x3 x-2
+
+C
3
2
C) -
B) -
8x 3 x-2
+C
3
2
D)
8x 3 x-2
+
+C
3
2
8x3 x-2
+C
3
2
te-7t2 dt
2)
A)
2)
1 -7t2
e
+C
14
Find the area between the curves.
3) y = x2, y = 4
32
A)
3
B)
1 -7t2
e
+C
7
C) -
31
B)
3
1 -7t2
e
+C
7
34
C)
3
D) -
1 -7t2
e
+C
14
37
D)
3
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
1
x
dx
4)
x+1
0
A) -1.33
B) -2.27
C) 0.39
D) -0.94
3)
4)
Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral.
1
dx
5)
5)
x2 - 49
A)
1
x-7
ln
+C
14
x+7
C) ln x +
B)
x2 - 49 + C
1
7+x
ln
+C
14
7-x
D) ln x +
x2 + 49 + C
Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by the curves.
6) f(x) = 3x + 2 , y = 0, x = 1, x = 5
6)
A) 44
B) 44
C) 80
D) 80
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
5
7)
1
8x(x + 1)2
A) -0.746
dx
7)
B) -5.965
C) 0.625
1
D) 0.120
Find the partial derivative.
z
.
8) Let z = g(x,y) = 9x + 7x2 y2 - 4y2. Find
y
A) 14xy2 - 8y
8)
B) 9 + 14xy2
C) 14x2y - 8y
Find the indicated relative minimum or maximum.
9) Minimum of f(x,y) = x2 - 14x + y2 - 16y,
subject to 2x + 3y = 12
A) f(1, 5) = -68
B) f(3, 2) = -61
D) 9 + 14x2 y
9)
C) f(2, 0) = -24
Evaluate the iterated integral.
2 5
(9x2 y + 5xy) dy dx
10)
0
0
85
A)
B) 85
2
D) f(0, 1) = -15
10)
C)
425
2
D) 425
Find the expected value of the probability density function to the nearest hundredth.
1
; [1, 4]
11) f(x) = 1 x
A) 2.83
B) 2.67
C) 3.00
11)
D) 2.50
Find all local extreme values of the given function and identify each as a local maximum, local minimum, or saddle point.
12) f(x, y) = 4 - x4 y4
12)
A) f(4, 4) = -65,532, local minimum
B) f(0, 0) = 4, local maximum; f(4, 4) = -65,532, local minimum
C) f(4, 0) = 4, saddle point; f(0, 4) = 4, saddle point
D) f(0, 0) = 4, local maximum
Evaluate the integral.
/12
tan4 3t dt
13)
- /12
2
A)
9 9
13)
B) -
4
9
C)
6
-
4
9
D)
6
Find the sum of the series as a function of x.
(x + 8)n
14)
n=1
A) -
x+8
x+9
14)
B) -
x+8
x+7
C)
2
x+8
x+9
D)
x+8
x+7
Find the derivative.
15) s = t5 - csc t + 18
ds
= 5t4 + csc t cot t
A)
dt
C)
ds
= t4 - cot2t + 18
B)
dt
ds
= 5t4 - csc t cot t
dt
D)
Find the Taylor series generated by f at x = a.
16) f(x) = x3 - 5x2 + 10x - 10, a = 5
A) (x - 5)3 - 10(x - 5)2 + 15(x - 5) - 40
ds
= 5t4 + cot2 t
dt
B) (x - 5)3 + 10(x - 5)2 + 15(x - 5) + 40
D) (x - 5)3 + 10(x - 5)2 + 35(x - 5) + 40
C) (x - 5)3 - 10(x - 5)2 + 35(x - 5) - 40
3
15)
16)
Purchase answer to see full
attachment