Answers for the last homework. Ripped straight from the solutions manual. If you want more
details on a specic problem, please email me.
16.7
2: 18 56.5
4: 80
4
8:
9 3+4 22
105
16: 241
5
1
17:
5+
48
2
Math 324E
1
Final Exam
Autumn 2005
(10 points)
Evaluate
y
1
xy dx + x2 dy,
2
C
where C is the curve given by r(t) = t, t2 1 for 1 t 1
x
2
and r(t) = 2 t, t + 4t 3 for 1 t 3. See the gure to
the right.
Math 324E
Your Name
Final Exam
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Total
Autumn 2005
50
Score
This exam is closed book. There is a page of formulas attached to the
Math 324E
1
(10 points)
Exam 2 Solutions
Autumn 2005
Evaluate
xey ds,
C
along the curve r( t ) = cos t, sin t, t from t = 0 to t =
2.
f ds =
f ( r( t ) r ( t ) dt. So then, r ( t ) = sin t, cos t, 1 ,
Math 324E
Your Name
Exam 2
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Autumn 2005
50
Score
This exam is closed book. You may use one hand-written 3x5 card for notes, though if
Math 324E
1
(10 points)
Exam 1 Solutions
Autumn 2005
Consider the function
f ( x, y ) = x4 2 x2 + y2 + 2
(a) Find the critical points of this function and classify them.
First nd the rst derivatives a
Math 324E
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Autumn 2005
50
Score
This exam is closed book and closed notes.
Only non-graphing scientic calculators a