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Math 220 Calculus I
Exam 2
Fall 13
Instructor: Robert Foth
Pima Community College, Community Campus
Answer the questions in the spaces provided on the question sheets. If you
need additional space use the back of the page and make sure the problem
number is referenced with the work. If scratch paper is used make sure to
attach the paper along with the exam when it is turned in. You must show all
work to receive full credit on the problem. You may use a calculator. Be sure
to read each question carefully and follow the instructions given.
Good luck!
All work on differentiating a function must be shown to receive credit. I am
looking for what you know (not what your calculator can do).
Students Name:________________________________________________________
1.
Find the derivative of the function given below. Make sure to show all the steps taken in the process.
f x 
8 cos  x 
8  x 
3
(8 points)
2.
Find the equation of a tangent line on the function
by
(8 points)
y  2x  3
f  x   2x2  3
that is parallel to the line given
3.
Write out the derivative in terms of f  x  and g  x  using the appropriate rules.
(4 points each)
(i)
h  x  f  x  g  x
(ii)
h  x 
4.
Write out the derivative in terms of f  x  and g  x  using the appropriate rules.
f  x
g  x
(6 points each)
tan  f  x  
(i)
h  x 
(ii)
h  x   eg x
 g  x  
2
f  x
5.
Consider the ellipse pictured below, which is given by the equation
x 2  xy  y 2  9
(8 points)
Find the equation of the tangent line to the ellipse at the y-intercept (0, 3) and draw it on the graph
above.
HINT: you must find dy/dx first.
6.
3
If f  x   x  4 x , then find and simplify lim
f  x   f  2
x2
x2
(8 points)
7.
Compute and simplify the second derivative with respect to x of y 
derivative before attempting the second derivative.
(8 points)
2x2
. Hint: Simplify the first
x2 1
8.
Use the definition of derivative to show that the derivative of f  x   3  4 x 2 is f '  x   8 x No credit
will be given if you don’t use the definition of derivative.
(8 points)
9.
(8 points)
Find the equation of the tangent line for the function f  x   3x 2  8 at the point (1,-5).
10.
Suppose that f  2   1, f '  2   3, g  3  2, g '  3  4, and g '  2   8. . Compute
h '  3 if h  x   f  g  x   . Hint: You may not need all of the given information.
(8 points)
11.
Find
dy
. Show your work. Do not try to simplify.
dx
(8 points each)
(i)
y   3 x  1 cos  5 x 
(ii)
y
2
ln  5  x 
x2