Math 205 Final Exam Review Solutions
2.5:19. The chain rule essentially says that D(f g ) = Df Dg , where the
right hand side indicates matrix multiplication. We use the notation that
x = st, y = tu, z = su (obtained from g ). Therefore,
D(f g ) = Df Dg =
Math 205: Midterm 2 Solutions
1. (15 points) Let f (x, y ) = x3/2 sin y .
a. Find the 2nd-order Taylor polynomial for f (x, y ) at the point (1, 0).
b. Use part (a) to approximate 1.13 sin(.1)
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p2 (x, y ) =f (1, 0) + fx (1, 0)(x 1) + fy (1, 0)(y 0) + fxx
Math 205 Midterm 2 Review
The exam will take place in class on Thursday, April 10, 2008. No books,
notes, or calculators are allowed. You will be held explicitly responsible for
the material we have covered since the last midterm, though much of that
depe
Math 205 Midterm 2 Review Solutions
1. p1 = 1 + 2x, p2 = 1 + 2x + 2x2 1 y 2 , e.2 cos .2 1.2.
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2. f (2, 2) is a minimum.
3. (I meant for this to be 2-d problem). Max temp is 4( 3 1)e4+2 3 .
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1
1
4. There are equilibrium points at (0, 0, 0), ( 2 , 2 ,
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Math 205: Midterm 1
March 6, 2008
The exam is all partial credit. Please write neatly and clearly, showing all of your work. No
calculators, cell phones, books, or notes may be used. The test contains 100 possible points. Good
luck!
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Math 205: Midterm 1 Solutions
1.
a.
b.
c.
Let a = (0, 3, 1), b = (2, 1, 1), c = (1, 1, 2).
(3a + b) c = 3(0, 3, 1) + (2, 1, 1) (1, 1, 2) = (1, 7, 4).
a b = (0, 3, 1) (2, 1, 1) = 0 2 + 3 1 + 1 1 = 4
Find the angle between the two vectors b and c.
b c = b c
Math 205 Midterm 1 Review
The exam will take place in class on Thursday, March 6, 2008. No books,
notes, or calculators are allowed. You will be responsible for the material
we have covered so far. While we have roughly covered 1.1-3.2, there are a
number
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Math 205: Final Exam
May 15, 2008
The exam is all partial credit. Please write neatly and clearly, showing all of your work. No
calculators, cell phones, books, or notes may be used. The test contains 130 possible points, and
you have 2.5 hours
Math 205 Final Exam Review
The nal exam will take place on Thursday, May 15, 2008 from 5:00 7:00 p.m. No books, notes, or calculators are allowed. You will be held
responsible for all the material we have covered this semester. The exam
will have a slight
Name:
ID:
Math 205: Midterm 2
April 10, 2008
The exam is all partial credit. Please write neatly and clearly, showing all of your work. No
calculators, cell phones, books, or notes may be used. The test contains 100 possible points. Good
luck!
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5
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