Write your name and student number on the front of your blue book
together with a grading table.
Start each question on a new page.
Make sure you SHOW ALL WORK. No points will be given for
answers where no justification is given.
- (16 points)
- From the definitions
and 
show that
- If
and 
, find
and 
.
Be sure to give exact answers (no decimal approximations).
- (16 points)
For both of the following, find
.
- (24 points)
Find the following limits
- (12 points)
In a colony of bacteria grown under ideal conditions the
rate of population growth at any time is proportional to the population
itself. Provide a differential equation for the population
at time t and write down its solution.
Initially a particular colony has 1250 bacteria. If the population
grows to 10 000 after 3 hours, when will it reach 40 000?
- (32 points)
Evaluate the following integrals
Extra Credit: (10 points) Find all x satisfying
