B. 
Show all work. A correct answer with no relevant working may receive no credit, while an incorrect answer accompanied by some correct work may receive partial credit.
I. Evaluate the following integrals. Show all steps.
A.II. Find the derivatives of the following functions. Again show all of your work.B.
A.III. Decide whether the following are true or false. As usual, show your work.B. y is the inverse function of f(x)=x+x³. Find y'(2). (Note that 2=f(1).)
A.IV. Given that
B.
grow at the same rate as
.
C.
implies that
.
D.
,
find
.
Your answer must be exact;
no decimal approximations.
V. Take derivatives to show that
for
.
What must C be?
VI. According to an Associated Press release from 1987, the world population had reached 5 billion persons. Five years later in the number had grown to 5.5 billion. Assume that the rate of change of the population at any given time is proportional to the population at that time. Answer the following questions.
A. What will the world's population be in the year 2000?B. When will the world's population reach 50 billion?
