MA108 – Hand-in Homework #2 – Fall 2011
Due Thursday, Oct 6 at 4:45 pm. Show you work!
1. Give an example of:
a. a rational function.
b. a quotient of two algebraic functions which is not a rational function.
c. a composition of a transcendental function followed by an algebraic function.
2. Let f (x) = 3x2 + 4 and g (x) = sin(2x). What are:
a. g f (x) ? b. f f (x) ? c. . f g ( /6) ?
3. Use our “new functions from old” ideas to draw careful graphs of:
a. y = -(x – 2)2 + 3 b. y = 4 cos(2x)
4. Find all t with 0 ≤ t ≤ 2 for which:
a. 2cos(t) = 1 b. (tan(2t))2 = 1 (This one has 8 solutions!)
5. Suppose .
a. What is the domain of f ?
b. What is the inverse f -1 of f ?
6. Evaluate: a. arcsin(1) b. arctan(-3) c. log10(10,000) d. log2(1/32)
7. Suppose a population P of spiders starts with 8 individuals and then triples every month.
a. Write down a formula for P in terms of t (the number of months which have
passed).
b. How many spiders will there be after 5 months?
8. You have a large piece of heavy wrapping paper which is 1/16 th of an inch thick. If you fold it in half 20 times, how many feet thick is the remaining object?
Reminder: Policy on Hand-in Homeworks
1. You should attempt to do the work on your own. You will learn the most that way.
Remember that you will have to do tests on your own!
2. If you do get help from someone else or work with someone else, that’s okay, but you must reference them - that is, write on your homework “I worked with Joe Blow on #7.” This will not affect your mark.
3. Late papers are accepted, but they lose 2 points for every calendar day of lateness.
4. Make an effort to hand in a neat, accurate piece of work. Have some pride in what you do!