Math 1134, Summer 12 Final Review
1 . A cube with sides 16 inches long is covered with a coat of berglass 0.2 inch thick. Use dierentials
to estimate the volume of the berglass shell.
2 . An egg of a particular bird is very nearly spherical. The radius to
Math 1134 Quiz 4 07/19/12 Answer
1) (10 points) Find local maxima, local minima, and saddle points of the function f (x, y ) = 2x2 +3xy +4y 2 +7x+11y .
Also, nd the corresponding function values.
Answer:
Set both fx (x, y ) = 0 and fy (x, y ) = 0.
fx (x,
Math 1134 Quiz 3 07/17/12 Answer
1) (6 points) Let f (x, y ) = xy + 6x 9y 40. Find all values of y such that f (y, y ) = 0.
Answer:
f (y, y ) = y y + 6y 9y 40
= y 2 3y 40
= (y + 5)(y 8)
So, y = 5, 8 are the solutions for f (y, y ) = 0.
3
2) (6 points) For
Math 1134 Quiz 2 07/03/12 Answer
dy
3
1) (6 points) Find the particular solution for the dierential equation:
= 3x2 ex ; y (0) = 4.
dx
Answer:
dy
3
= 3x2 ex
dx
3
dy =
3x2 ex dx
y=
3x2 ex dx
Substitute u = x3 , then du = 3x2 dx, so dx =
3
1
du,
3x2
y=
=
an
Math 1134 Quiz 1 06/26/12 Answer
x
1) (4 points) Find dy for the function: y = x5 45
.
7
Answer:
1
y = 45x5 x6
7
1
4
dy = 225x (6x5 ) dx
7
2) (7 points) Find the indenite integral:
5 y2
dy .
2y
Answer:
5 y2
dy =
2y
5
y2
dy
2y 2y
51
1
=
y dy
2y
2
1 y2
5
Math 1134, Summer 12
Name:
August 1, 2012
OSU ID (Lastname.XXX):
Midterm 2
Instructions:
You have 55 minutes to complete this exam. It consists of 6 problems on 7 pages including this
cover sheet and is worth a total of 100 points. The value of each ques
Math 1134, Summer 12 Midterm 2 Review
1 . Let f (x, y ) =
x2 y 3
+ (x2 y + 1) ln(3 + x3 ), nd fx (x, y ) and fy (x, y ).
4 y2
2 . Find all the critical points of the following function. By using the Second Derivative Test,
determine whether the critical p
Math 1134, Summer 12
Name:
July 9, 2012
OSU ID (Lastname.XXX):
Midterm 1
Instructions:
You have 50 minutes to complete this exam. It consists of 7 problems on 8 pages including this
cover sheet and is worth a total of 100 points. The value of each questi
Math 1134, Summer 12 Midterm 1 Review
1 . A cube with sides 15 inches long is covered with a coat of berglass 0.3 inch thick. Use dierentials
to estimate the volume of the berglass shell.
2 . For a company that manufactures tennis rackets, the average cos