Mathematics 2122-001
Calculus for Life Sciences II
Fall 2002
Study Guide for Test #1
Instructor: Dr. Alexandra Shlapentokh

1. Differentiate the following functions.
(a)
(b)
(c)
(d)
(e)
2. Graph the following functions
(a)
(b)
(c)
(d)
(e)
(f)
3. Convert into radians.
4. Convert 5 radians into degrees.
5. 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) ?
6. 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) ?
7. Suppose the hypotenuse of a right triangle is 2 in and one of the angles is . What are the lengths of the legs?
8. Suppose a point corresponding to an angle on the unit circle is in the first quarter. Assume further that . What is the value of
(a) ?
(b) ?
9. Determine if the following equalities are true for all measured in radians.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) .
10. Compute the following limits.
(a)
(b)
(c)
(d)
(e)