Calculus III: Practice Midterm I
Name:
Write your solutions in the space provided. Continue on the back if you need more
space.
You must show your work. Only writing the nal answer will receive little credit.
Partial credit will be given for incomplete
Final Exam for Calculus 111
June 21., 2012
NAME:
UNI:
Directions
0 The exam is 3 hours.
0 There are 8 problems in total with each for 5 points. Please
check that there is no page missing before you start.
0 No textbooks, HW. notes, calculator, laptop
1. Find an equation of the set of points such that its distance to
the place 8 : 2:1: + 2y z + 1 = 0 is equal to its distance to the point
P : (1,1,1).
94 . A§SUMQ guk 0L YoM @ (5 4 (Dothng (90 1?)
41324:
ll'X'hj-zg(H izx+zjv3+r(
\ v _.r.
A§t(G,'S)-C'- my
Calculus III: Practice Midterm I
Name:
Write your solutions in the space provided. Continue on the back if you need more
space.
You must show your work. Only writing the nal answer will receive little credit.
Partial credit will be given for incomplete
Calculus III: Practice Midterm II
Name:
Write your solutions in the space provided. Continue on the back if you need more
space.
You must show your work. Only writing the nal answer will receive little credit.
Partial credit will be given for incomplet
Calculus III: Practice Midterm II
Name:
Write your solutions in the space provided. Continue on the back if you need more
space.
You must show your work. Only writing the nal answer will receive little credit.
Partial credit will be given for incomplet
Calculus III: Practice Final
Name:
Circle one:
Section 6
Section 7
.
Read the problems carefully.
Show your work unless asked otherwise.
Partial credit will be given for incomplete work.
The exam contains 10 problems.
The last page is the formula she
PRACTICE MID TERM I
CALCULUS III
The use of class notes, book, formulae sheet, calculator is not permitted.
In order to get full credit, you must show all your work.
Each solution must have a clearly labeled problem number and start at the top of a
new
MID TERM I
CALCULUS III (26660 SEC. 2)
The use of class notes, book, formulae sheet, calculator is not permitted.
In order to get full credit, you must show all your work.
You have one hour and fteen minutes.
Do not forget to write your name and UNI i
Name:
Solutions to Practice Final
1. Consider the line r(t) = 3 + 2t, 2 t, 6 .
(a) Find symmetric equations for this line.
(b) Find the point where the rst line r(t) intersects the surface z = x + y 2 .
Solution.
(a) We have x = 3 + 2t, y = 2 t, z = 6 so
Calculus III: Practice Final
Name:
Circle one:
Section 6
Section 7
.
Read the problems carefully.
Show your work unless asked otherwise.
Partial credit will be given for incomplete work.
The exam contains 10 problems.
The last page is the formula she
Name:
Practice Final
1. Consider the line r(t) = 3 + 2t, 2 t, 6 .
(a) Find symmetric equations for this line.
(b) Find the point where the line r(t) intersects the surface z = x + y 2 .
2. Consider the two lines r(t) = 1 + t, 2 + t, 3 t and s(t) = t, 1 +
Final Exam for Calculus III
June 21, 2012
NAME:
UNI:
1
2
3
4
5
6
7
8
total
Directions
The exam is 3 hours.
There are 8 problems in total with each for 5 points. Please
check that there is no page missing before you start.
No textbooks, HW, notes, calcu