MATH 203 Spring 2009
FINAL EXAM
10 problems, 10 points each
Instructions:
Show enough work to justify your answers
Suppose you have a function

Evaluate this limit:

What
is it that you've
found?
Evaluate the derivative of


Find the derivative of


Find the second derivative of

What does it tell you about the shape of the graph of


The graph of a function

is given below. Estimate the values of the derivative

for

and




The graph of

is given below. Describe the behavior of the function using:
"increasing/decreasing on interval..", "concave up/down on interval..",
"max/min at..", "asymptotes are..",
etc.

Evaluate the integral:



Find the area of the region bounded by

the

-axis,
and the lines

and


Draw a few level curves of the function


Find all critical points of the function
