NAME:
MA 23200 Sample Final Exam
PUID: INSTRUCTIONS There are 25 problems on 14 pages. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded. No books or notes are allowed. You may use a one-line scie
MA 232
Calculus II Group Work Solutions (L4-L5)
Fall '10
1. Find the general form of the integral using integration by parts twice. x2 cos(x) dx Solution: x cos(x) dx = x sin(x) -
2 2
2x sin(x) dx - cos(x) 2 dx]
u = x2 dv = cos(x) dx du = 2x dx v = sin(x)
7
1. Perform Gauss-Jordan elimination on the following matrix. I am grading your
work not just your answer so be clear what you are doing and write legibly.
(20 pts)
12
A:L;
A-
-F3+sr4 lZ
l-e+rz-rl Z
O
o
L,+
-f
-t
I
4
il
IN
0'l
- (r+C1a
t*tt )
lz
loo
o
La
MA 23200: Calculus for the Life Sciences II Fall 2010
COURSE WEBPAGE: http:/www.math.purdue.edu/ma232 REQUIRED TEXTBOOK: Calculus for the Life Sciences, Marvin L. Bittinger, Neal Brand and John Quintanilla, 2006 PREREQUISITE: MA 23100 (or: MA 29000 Sectio
MA 232
Calculus II
Fall 10
Quiz 3:ANSWERS (L5)
Show work and have the right answer for full credit. Wrong answer with some right work is
worth partial credit, and right answer with wrong work is worth partial credit.
1. Find the value of the integral.
5
l
MA 232
Calculus II Quiz 2 (L3)
Fall '10
Show work and have the right answer for full credit. Wrong answer with some right work is worth partial credit, and right answer with wrong work is worth partial credit. 1. Find F () if F () = cos sin2 and F (0) = 2
MA 232
Calculus II
Fall 10
Quiz 2:ANSWERS (L3)
1. Find F () if
F () = cos sin2
and F (0) = 2/3 .
Solution:
By the Fundamental Theorem of Calculus, we can nd F () by
integrating F () = F () d. So,
F () =
=
cos sin2 d
u = sin
u2 du
du = cos d
= 1/3 u3 + C
MA 232
Calculus II Quiz 1 (L1)
Fall '10
Show work and have the right answer for full credit. Wrong answer with some right work is worth partial credit, and right answer with wrong work is worth partial credit. 1. Find the area under f (x) = and over the i
MA 232
Calculus II
Fall 10
Quiz 1: ANSWERS (L1)
Show work and have the right answer for full credit. Wrong answer with some right work is
worth partial credit, and right answer with wrong work is worth partial credit.
1. Find the area under
f (x) =
ex
x1
MA 232 - Quiz 1 (10 minutes)
Friday, January 11th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (10 points) Evaluate.
4 points for simplifying
(sec + tan ) sec d
Solution : (sec + tan ) sec d = (sec2 + tan sec )d =
tan
MA 232 - Quiz 2 (15 minutes)
Friday, January 16th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (10 points) Evaluate.
cos t
dt
2 points for u
esin t
2 points for du
Solution : If we choose u = sin t then du = cos t dt
MA 232 - Quiz 2 (15 minutes)
Friday, January 25th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (10 points) Evaluate.
2 e 3 d
1 point for
Solution : Recall udv = uv vdu. We apply integration by parts
u,dv
v,du
with u
MA 232 - Quiz 12 (15 minutes)
Wednesday, March 27th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (10 points) Solve the following initial value problem explicitly for y
xdx + y sec xdy = 0, y ( ) = 0.
Solution : The eq
MA 232 - Quiz 11 (12 minutes)
Wednesday, March 20th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (8 points) Find the integrating factor for the following dierential
equation
(cos x)y + (sec x)y = cot x, 0 < x < .
2
A.
MA 232 - Quiz 10 (15 minutes)
Wednesday, March 6th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (6 points) Find the particular solution of the following dierential
equation:
2 points for
each
antiderivative
1 point fo
MA 232 - Quiz 9 (Due 2/25/13 by 2:35pm)
Friday, February 22nd, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (6 points) Problem 8. Page 534.
2 points
for the
s lope
Solution : The regression line is y = .227x 357.556.
2
MA 232 - Quiz 8 (10 minutes)
Monday, February 18th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
4 points for 1.
s tating that
the mixed
partials are
equal
(8 points) If fx = g and gyy = 0. Then fyxy ? Justify your answer
MA 232 - Quiz 7 (15 minutes)
Monday, February 15th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (8 points) f (x, y ) = 2xy + 6x + 2y 8. There is a critical point at
A. (3, 1)
B. (1, 3)
C. (3, 1)
D. (1, 3)
E. (1, 3)
So
MA 232 - Quiz 6 (15 minutes)
Monday, February 11th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (8 points) Let f (x, y ) = y ln(xy ). Find fy (2, 3).
A. ln(6) + 1
3
9
B. ln(6) + 2
C. ln(6) + 1
D. ln(6) + 5
2
3
E. ln(6
MA 232 - Quiz 5 (7 minutes)
Wednesday, February 6th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (16 points) The equation for a sphere of radius 5 centered at the origin
is given by the equation x2 + y 2 + z 2 = 25. F
MA 232 - Quiz 4 (20 minutes)
Wednesday, January 30th, 2013
The maximum quiz score is 20 points.
Please read all questions carefully.
1. (8 points) The curve y = x + ex, 0 x 2, is rotated about the
x-axis. Which integral gives the volume of the solid of re
MA 232
Calculus II
Fall 10
Practice Quiz 5 (L11)
Show work and have the right answer for full credit. Wrong answer with some right work is
worth partial credit, and right answer with wrong work is worth partial credit.
For each given function f (x, y ), n
MA 232
Calculus II Practice Quiz 4 (L7)
Fall '10
Show work and have the right answer for full credit. Wrong answer with some right work is worth partial credit, and right answer with wrong work is worth partial credit. 1. Find the area of a sphere of radi
MA 23200
1. Evaluate
Final Exam
3
1
dx.
2x
3
A. (2 x)2/3 + C
2
B.
3
(2 x)2/3 + C
2
C.
3
(2 x)1/3 + C
2
D. 3(2 x)1/3 + C
E. 3(2 x)1/3 + C
2. Find the area under the graph of f over the interval [1, 3], where
f (x) =
2x,
4x,
A. 16
B. 18
C. 20
D. 24
E. 32
1
MA 23200
Exam 3
1. (12 points) Solve the initial value problem xy + 4x2 y = x2 , y (1) = 0.
2. (12 points) Solve the dierential equation y = ln(xy ).
1
April 12, 2010
MA 23200
Exam 3
3. Consider the initial value problem y +
y
2x3
April 12, 2010
= 1, y (6
MA 23200 Exam 3 Solutions
Doug Babcock
14 April 2010
Problem 1
Dividing the dierential equation by x gives:
y + 4xy = x
We can solve this using the method for linear dierential equations. Integrating 4x gives
2
2x2 . Thus, we should multiply both sides of
Exam #3 Review Problems
Doug Babcock
5 April 2010
1. Consider the initial value problem xy + y = ln(10 x), y (1) = 0. Find the largest interval
on which a solution to this initial value problem is guaranteed to exist.
2. Consider the initial value problem
MA 23200
Exam 2
1. If f (x) = 5x 2xy 2 + ey3 , then f (2, 3) is
A. e 10
B. 10
C. e 11
D. 11
E. 12
2. If f (x, y ) = sin(xy ) + x2 y + 5xy 3 , then fx (x, y ) is
A. y cos(xy ) + 2xy + 5y 3
B. y cos(xy ) + x2 + 15xy 2
C. x cos(xy ) + 2xy + 5y 3
D. x cos(xy