M161- Survey of Calculus
Section 09
Exam 1
Name:________________________________________
No calculators. You must show all work for full credit.
1. (2 points each)
Evaluate the following limits using the graph above:
a.
b.
c.
d.
e.
f. (3 points) Is
continuous.
continuous at
? Explain why or why not using the definition of
g. (3 points) Is
continuous.
continuous at
? Explain why or why not using the definition of
2. (4 points each) Find each of the following limits, or state that it does not exist.
a.
b.
c.
d.
e.
3. (15 points)
a. Use the limit definition of the derivative to find the derivative of
b. Find the slope of the line tangent to
c. Write the equation of the line tangent to
at the point
at the point
.
.
4. (5 points each)Find the derivative of each function (don’t simplify all the way).
a.
b.
c.
d.
5. (9 points)
Find the second derivative of
6. (10 points)
Use implicit differentiation to find
of
7. (10 points)
On Halloween night, Charlie Brown’s friend
Linus is waiting in the local pumpkin patch to
catch the Great Pumpkin as it rises from the
pumpkin patch to bring all good calculus
students candy.
He spots the Great Pumpkin 12 feet away, just
as it is starting to rise. If the pumpkin is rising at a rate of 3 feet per minute, how fast is
the distance between the pumpkin and Linus changing when it has risen 5 feet off the
ground?