finalguideh.htm

Mathematics 2122-001
Calculus for Life Sciences II
Fall 2003
Final Study Guide
Instructor: Dr. Alexandra Shlapentokh

Compute the following limits.

(a)
(b)
(c)
(d)
(e)

A certain variable varies sinusoidally between 1 and 3 with a period of 2 days. The variable reaches its highest value at 1 PM of the first day. Find a formula for

What is the degree of the trigonometric polynomial

What is the amplitude of the following periodic function

What is the period of the function

What is the period of the function

What is the period of the function

What is the period of the function

Suppose an antiderivative of

Suppose one antiderivative of

. Describe all the other antiderivatives of

Suppose an antiderivative of

and antiderivative of

then what’s an antiderivative of

(a)	?
(b)	?

Suppose antiderivative of

is a differentiable function. Then what is the antiderivative of

What are the antiderivatives of the following functions?

(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)

Use the table on page 649 to evaluate the following integrals.

(a)
(b)

Compute the following definite integrals.

(a)
(b)
(c)
(d)
(e)	.

Find the following areas.

(a)	The area under and above between and .
(b)	The area bounded by .
(c)	The area bounded by the curves and .

Find the distance between the points with coordinates

What is the formula of the sphere centered at (1,2,3) and of radius equal to 5?

What is the graph of the equation

Find the domain of

Find the domain of

Find the domain of

for the following functions:

(a)
(b)
(c)

Classify the following equations as to their order, linearity/non-linearity, and as to whether they have constant coefficients. In all the problems below assume that

is a function of independent variable

(a)
(b)
(c)
(d)

Solve the following differential equations:

(a)	.
(b)	.
(c)	.
(d)

A certain population of bacteria, as a function of time measured in hours, is growing at the uniform rate equal to 2% of the population size. Suppose that the initial population contains 1000 cells. What will the population be at time

A population of rabbits on an island triples every 5 years. How long does it take this population to double if the growth rate is always proportional to the population size?

If a radiation dose of 1 rad kills 3% of cancer cells, how much radiation would kill 99% of the cells? (Assume that cancer cell death rate is always proportional to the number of cells.)

Suppose a certain radioactive element has a half-life of 1000 years. How long before 99 % of the original amount is lost?

Suppose a certain population of animals has a uniform birth rate of 20% with 2 young surviving per birth on the average and a uniform death rate of 10% when time is measured in years. What is the population size as a function of time, if the initial population was 200 animals?

Solve the following equations.

(a)	.
(b)
(c)
(d)

Suppose a certain population of animals has a uniform birth rate of 20% with 2 young surviving per birth on the average and a uniform death rate of 10% when time is measure in years. Assume also that each year 100 animals are moving into the area. What is the population size as a function of time, if the original population was 200 animals?

Solve the following equations.

(a)	, .
(b)	, .
(c)	,
(d)	,
(e)
(f)

Suppose a population of mice in a house follows a logistic model with the maximum population equal to 300 mice. Initially the house had 10 mice. After 1 year the house had 50 mice. How many mice will live in the house after 5 years?