Math 141, Final Exam, 2000
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There are 19 problems on 9 pages. Problem 1 is worth 20 points, each of the other
problems is worth 10 points. SHOW your work. CIRCLE your answer. NO
CALCULATORS!
1. (The penalty for each mistake is five points.) The picture represents the graph
of y=f(x).
(a) Fill in the blanks:
f(1) = lim
x→1+f(x)= lim
x→1−
f(x)= lim
x→1f(x)=
f(2) = lim
x→2+f(x)= lim
x→2−
f(x)= lim
x→2f(x)=
f(3) = lim
x→3+f(x)= lim
x→3−
f(x)= lim
x→3f(x)=
(b) Where is fdiscontinuous?
(c) Where is fnot differentiable?
2. What is the derivative of f(x)=2x
5+3
√
x+4x
2+10?
3. Use the DEFINITION of the DERIVATIVE to find the derivative of f(x)=x
2.
4. What is the equation of the line tangent to f(x)=2x
3−2 at the point where
x=3.
5. If y=(5x3+9x)2
sin(7x2−15x), then find dy
dx .
6. Find dy
dx for 6x2y2+2x=cosy.
7. A man, who is 6 feet tall, is walking, at the rate of 3 ft./sec., away from a light
pole, which is 25 feet high. How fast is his shadow growing when he is 30 feet
from the light pole?
8. DEFINE the definite integral Rb
af(x)dx.
9. Find Z(2x4+√3x−2)dx . Check your answer.
10. Find Zxcos(5x2+ 18) dx . Check your answer.
11. Find Z1
0
5xp3x2+4dx .
12. Let f(x)=x
3−3x. Where is f(x) increasing, decreasing, concave up, and
concave down? Find the local maximum points, local minimum points and the
points of inflection of y=f(x) . Find the vertical and horizontal asymptotes
of y=f(x). GRAPH y=f(x).
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