MA 125 Fall 2005 Final Examination
Part One
There are ten Part One problems, worth 4 points each. Place your answer
on the line to the right of the question. Space is provided between problems
for you to work each problem, but no partial credit will be given on Part One
problems, and only your entry on the answer line will be graded.
1. Determine
lim
x!1
2x3x2+ 1
5x3+x+ 9 :
2. Determine
lim
x!0
1cos(x)
x2:
3. Let f(x) = xcos(x). Determine f0(x).
4. Let f(x) = esin(x). Find f0(x).
5. Let
g(x) = px
1 + x:
Find g0(x).
6. Let f(x) = (ln(2x))4. Find f0(x).
7. Let f(x) = exg(x). Find f0(0) if g(0) = 2 and g0(0) = 5.
8. Let g(x) = x424x2+ 6x8. Find all open intervals on which the graph
of gis concave down.
9. Evaluate R=4
0cos(x)dx.
10. Evaluate R(1 + 4x2)dx.
Part Two
There are six Part Two questions, each worth ten points. A page is provided
for you to work each problem. Attach additional pages if they contain material
you judge to be an important part of your solution. Your solution must include
enough detail to justify any conclusions you reach in answering the questionh.
Partial credit may be awarded on Part Two problems where it is warranted.
1. (a) Find y0if y(x)is de…ned implicitly by the equation x2y2+ 2xy
2x4y+ 9 = 0.
(b) Find the equation of the tangent to the graph of this equation at (2;3).
(c) Find the xcoordinate of each point on the graph of this equation at
which the tangent is horizontal, or show that there is no such point.
2. Calculate the area bounded by the xaxis and the graph of y=x3x
for 1x2.
3. Let f(x) = 3x55x3.
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