Mathematics 2122-001
Calculus for Life Sciences II
Spring 2005
Study Guide for Test #1
Instructor: Dr. Alexandra Shlapentokh
1. Differentiate the following functions.
(a)
(b)
(c)
(d)
2. Graph the following functions
(a)
(b)
(c)
(d)
3. What is the range of
(a) ?
(b) ?
(c) ?
(d) ?
4. What is the domain of
(a) ?
(b) ?
(c) ?
(d) ?
5. If is a point on a unit circle and is the radian measure of the acute angle . Then the -coordinate of corresponds to what function of ?

6. Convert into radians.
7. Convert 5 radians into degrees.
8. What is the length of the arc of a circle of radius 2 in, if the central angle corresponding to the arc is
(a) radians?
(b) ?
9. What is the area of the sector of a circle of radius 2 in, if the central angle corresponding to the arc is
(a) radians?
(b) ?
10. Suppose the hypotenuse of a right triangle is 2 in and one of the angles is . What are the lengths of the legs?
11. Find the following values, if the angles are measured in degrees.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
12. Find the following values, if the angles are measured in radians.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
13. 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 .
14. What is the amplitude of the following periodic function ?
15. What is the amplitude of the function ?
16. For what value of does the function achieve the highest value?
17. What is the period of the function ?
18. What is the period of the function ?
19. For what values of , does attain its highest and lowest values?
20. Suppose is an antiderivative of , then what is ?
21. Suppose an antiderivative of is . Describe all the other antiderivatives of .
22. Suppose an antiderivative of is and antiderivative of is then what’s an antiderivative of
(a) ?
(b) ?
23. What are the antiderivatives of the following functions?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
24. Suppose the velocity of a particle moving along a straight line is . What is the distance travelled by the particle between and ?