MATH-2450Name ______
Sample Exam 2 Form A
Fall 2000S.I.D.# ______
Directions: You must show enough work to justify your answer on ALL problems. Correct answers with no work (or inconsistent work) shown will not receive any credit. All answers are to be exact; no decimal approximations. The point value for each problem is given.
1.Differentiate the following functions. Put a box around your final answer.
a. (6 pts.)
b. (Simplify your answer.) (8 pts.)
c. (Simplify your answer.) (9 pts.)
d. (8 pts.)
e. (Do not simplify your answer.) (8 pts.)
2.Find the critical number(s) of the function (10 pts.)
Answer ______
3.If , then find . (8 pts.)
Answer ______
4.Find the slope of the tangent line to graph of at . (6 pts.)
Answer ______
5.If is the position function which gives the position (in yards) of a particle at
time t (in sec.), then find the acceleration of the particle when t = 3 sec. (8 pts.)
Answer ______
6.Given the function find the following: (15 pts.)
a.Critical number(s) ______
b.Interval(s) on which g is increasing ______
c.Interval(s) on which g is decreasing ______
d.Local minimum(s) ______
e.Local maximum(s) ______
7.A girl flying a kite pays out string at a rate of 4 ft/min as the kite moves horizontally at an altitude of 40 yards. Assuming there is no sag in the string, find the rate at which the kite is moving when 160 feet of sting have been payed out. (10 pts.)
Answer ______
8.Gas is leaking out of a spherical balloon at a rate of 2 cm 3 /sec. Find the rate at which the radius of the balloon is changing when the volume of gas in the balloon is 36π cm 3. (8 pts.)
Volume of a sphere:
Answer ______
9.An airplane is flying at altitude of 5 miles toward an observer on the ground. The angle of elevation from the observer to the plane is increasing at a rate of 3 per minute. Find the rate of the plane when the plane is directly over a point on the ground that is 2 miles from the observer. (10 pts.)
Answer ______