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Final Exam Fall 2008/2009
U A E University, College of ScienceDepartment of Mathematical Sciences
MATH 1110 CALCULUS I FOR ENGINEERS
8/1/2009 5-7 pm
Student’s Name Student’s I.D. Section #
Circle the name of your instructor (with the time of your class)
Exam regulations:1) This exam consists of 10 problems and 11 pages including this cover page.2) The time limit is 120 minutes.3) Only regular scientific calculators are allowed, but may not be shared.4) Show all your work in order to qualify for full credit.
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
Dr. Tarik Ali - Section 51 Dr. Jae Lee - Section 01
Dr. Tarik Ali- Section 52 Dr. Jae Lee - Section 02
Dr. Sherif Moussa - Section 53 Dr. Adama - Section 03
Dr. Sherif Moussa - Section 54 Dr. Adama - Section 04
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Problem 1: (4 points)Multiple Choices Problems. Circle only one for each problem.
i) Find the second-degree polynomial (of the form ax2 + bx + c) such that
f(0) = 0, f '(0) = 5, and f ''(0) = 1.
A) B)
C) D)
ii) The interval(s) where is increasing and/or
decreasing
A) increasing and ; decreasing B) increasing ; decreasing
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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C) increasing and ; decreasing and D) increasing ; decreasing and
Note: The Sign chart of f’(x) for C.P. (-1,+1)------+----(-1) --------(0)--------(+1)---+---According to the point x=0 is not in our domain, but he mentioned in the one of the choices.
iii) An antiderivative of is:
A) B)
C) D)
iv) If the acceleration vector is , the initial velocity is
, and the initial position function is then the position vector is:
A) B)
C) D)
Problem 2: (4 points) Answer True or False for the following statements: Put T for the correct statement and F for the false statement:
i) The graph of the area bounded by the curves
is [T]
ii) The graph of has absolute max: and absolute
min: on the interval . [ F ]
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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( the first part is true, but the second one, it has to be (0,0))
iii) If the unit price of units of a certain product is given by ,
then the maximum possible revenue when selling x units to nearest dollar is . [ T ]
Revenue (R)= PQ= P X, find R’. Then, solve for x=Sq(50)-3=4.07, Rmax =Px ( when x=4.07)iv) The area between the and the graph of the function
from to is [ F ]
Problem 3: (3 points)
In statistics, the function is used to analyze random quantities that
have a bell-shaped distribution. Solutions of the equation give statisticians a measure of the variability of the random variable.
1. Find
2. Find all the solutions such that .
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Problem 4: (4 points)
1. Find the point on the curve closest to the point
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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2. Find an equation of the tangent line to the graph of at if
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Problem 5: (3 points)Consider the curve 1. Use implicit differentiation to find 2. Find all points such that .3. Are all the solutions of question (2) lying on the curve
? Explain.4. Is there any vertical or horizontal tangents? Explain.
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Problem 6: (3 points)Suppose that you are blowing up a balloon by adding air at the rate of . If the balloon maintains a spherical shape, the volume and the radius are related by
. Compare the rate at which the radius is changing when and
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Problem 7: (5 points)
a) Evaluate the integral .
b) Decompose the rational function into partial fractions, then
evaluate , where is a constant.
Now,
Problem 8: (5 points)
Evaluate the following integral
a) .
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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b)
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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Problem 9: (4 points)
a) Sketch and find the area of the region determined by the intersections of the curves: .
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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b) If , compute .
Problem 10: (5 points)
a) Compute the volume of the solid formed by revolving the region bounded by
and about .
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
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b) Compute the volume of the solid formed by revolving the region bounded by
and about the
Final Exam (Fall 2008/2009) Math 1110 CALCULUS I FOR ENGINEERS.
