22M:016 Calculus for the Biological Sciences – Final Exam
1. Compute the derivative of 
from the definition.
2. Find the equation of the tangent line to 
at 
.
3. A population of bacteria divides on the average every two hours. If the
initial population is 
, when will the population be 
?
4. Use differentials to approximate 
.
5. Find the inverse of 
.
6. Using the properties of logarithms, find exactly
(a) 
(b>0)
(b) 
7. Using calculus, sketch the graph of 
. Determine
where f is increasing/decreasing, concave upward/downward, inflection
points and local and absolute extrema.
8. A forestry company plans to log a certain area of fir trees. The average number of board feet obtained per tree is 50-0.5x where x is the number of trees per acre with 
. What density of trees should be maintained to maximize the number of board feet per acre?
9. Find the area bounded by the curves 
and 
.
10. Use the Second Derivative Test to find the local extrema of 
.
11. Find the following limits
(a) 
(b) 
12. (a) 
(b) 
13. Computations
(a) 
(b) 
(c) 
(d) 
(e) 