Superb Professors

1) Consider the function

a) Determine whether the Mean Value Theorem applies on the given interval.
b) If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.
2) Given
a) Write the equation of the line that represents the linear approximation to the function at the given point .
b) Use the linear approximation to estimate the given quantity.
3) Determine the location and value of the absolute extreme values of on the interval
4) Given

a) Find the intervals of increase and decrease.
b) Find the local extreme value(s).
c) Find the intervals of concave up and down.
d) Find the inflection point(s).
e) Find the asymptote(s).
f) Sketch the graph.
5) What point on the line is closest to the origin?
6) Evaluate the following limits. Use L’Hopital’s Rule when it is convenient and applicable.
a)

b)

c)

7) Find the antiderivative of each function.
a)
b)

8) Determine the following indefinite integral.
 
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