Math 1100
Chapter 9 Review
23 September, 2013
Name:
1. List the three most important things you have learned so far in this class.
• important thing!
• important thing!
• important thing!
2. Compute each limit.
(a)
lim x3 − 6x + 1
x→2
(b)
x2 + 5x − 6
x→1
x−1
lim
3. List as many words or phrases as you can think of that mean “derivative.”
4. (a) Write the definition of a derivative. (This will involve a limit.)
(b) Use this definition to compute the derivative of f (x) = 2x2 .
5. Find the equation of the line tangent to y =
x+5
x−2
at the point (1, −6).
x2 + 1 if x ≤ 1
3x − 2 if x > 1
Is f (x) continuous at x = 1? Explain your answer in detail.
6. Let f (x) =
7. Suppose the profit in dollars for a company producing x gallons of maple syrup is
P (x) = 40x − .06x2
(a) Find P (100). What does this represent?
(b) Find P 0 (100). What does this represent?
(c) Use P 0 (100) to estimate the total profit from producing 110 gallons of maple syrup.
(d) Find the actual profit from producing 110 gallons of syrup.
8. Differentiate each function.
(a)
y=
√
6
+ 3x
3
x
(b)
1
f (x) = √
x+4
(c)
r(b) =
√ 8
b(b + 4)