MATH 161 - EXAM I
NAME ____________________
DO NOT SIMPLIFY YOUR ANSWERS
1. (5 points each) Find each of the following limits (if it exists):
a) lim
2x + 1
b) lim
x 2
x 3
x1
c) lim
x ∞
x2 + 9
x2  x  6
2x3 + 9_
4 x3 + 3
d) Let
2. (10 points) For the equation f (x) = 4x2  x find the equation of the tangent line at x = 1
3. (10 points) Use the limit definition of the derivative to find the derivative of
4. (10 points each) Differentiate each of the following:
a)
+5
b)
c)
d)
5. (10 points) Use implicit differentiation to find dy/dx when x3 y + y2 – 5x2 = 4
6. (10 points) A cylindrical tank stock has a height of 6 feet and its radius of 4. Water is being pumped into the tank.
The height of the water in the tank is rising at a rate of 2 feet per hour. How fast is the volume of the tank increasing?
(Hint: V=πr2h)