MATH 221 Final Exam Part 1 Name___________________
Instructions: Answer all the questions on Part 1 and place your answers in the appropriate spaces. You may not use a calculator on this section. (5 points apiece)
1. Find 
each of the following:
a) 
a)________________
b) 
b)________________
c) 
c)________________
d) 
d)________________
2. Find each of the limits:
a) 
a)__________________
b) 
b)__________________
3. Evaluate the following integrals:
a) 
a)__________________
b) 
b)________________
MATH 221 Final Exam Part 2 Name___________________
Instructions: Answer any 5 of the 6 questions on this part. You may use a calculator on this part. (20 points apiece)
1. Let
. Find 
using the limit definition of the derivative.
2. Solve the following inequalities and put your solutions in interval form.
a) 
b) 
3. a)
Let L and M be the tangent lines to the graph of 
at the points corresponding to x = 1 and x = -1
respectively. Find the point of
intersection of L and M and show that L and M are perpendicular.
b) Find the
equations of all lines tangent to 
that pass through the
point (2,-2).
4. Let
. Let R be the region
bounded the graphs of f(x) and g(x).
a) Find the area of R.
b) Find the volume of the solid that results if R is rotated about the y-axis.
c) Find the volume of the solid that results if R is rotated about the x-axis.
d) Find the length of the graph of f(x) from x = 1 to x = 5.
5. A closed rectangular box is to be constructed so that the length of its base is three times the width of its base. If the box is to be constructed from 1,800 square inches of sheet metal, what dimensions will give a box of maximum volume?
6. Find and classify the critical points of each of the following functions:
a) 
b) 
c) 