1.(4 pts each) Determine the exact value for each of the following limits:
2.(4 pts each) Determine derivatives (with respect to x) for the following:
( ) 4 5lnf x x x=+
h x x e=
e.Determine the partial derivative with respect to x
3. (4 pts each) Integrate the following:
Part II: Calculators allowed on this part, but still make sure you show your work!
4.(6 pts) For the function
a.Determine the average rate of change from
b.Determine the instantaneous rate of change at
5.(6 pts) Determine the equation of the tangent line at
6.(6 pts) For
( ) 2 12f x x x= - +
, use calculus to determine the location of:
a.Any maximum or minimum points (tell which are max and which are min)
b.Any inflection points
7.(6 pts) A store owner currently sells an item for $20 and can sell 200 items per
week on average. However, market research says that for each $2 decrease in
price, the owner will be able to sell 25 more items per week. Use calculus to show
what price should the owner set so that the weekly maximum revenue is realized.
8.(6 pts) Let ()Px be a function which describes the relationship between the
number of items sold x and the profit P from selling x items.
(100) 800P = as it applies to the description above.
a.Explain the meaning of the equation (100) 10P = as it applies to the description above.
b.Explain the meaning of the equation
9.(6 pts) Under certain conditions, the number of cancer cells
()Nt at time t increases at a rate of N t e = Suppose that at 5 days, the number of cells is growing at a rate of 150 cells per day. Determine a number of cells after 14 days
'( ) 50
if there were 100 cells initially.
10.(12 points) Assume the revenue generated from a basketball game is given by
( , ) 5 3 1.5R c t t c c t= + +, where c is the number of open concession stands and t
is the number of tickets sold to the game.
a.Calculate (10, 200)R and explain it’s meaning in the context of this
b.Calculate R and explain it’s meaning in the context of this
11.(6 pts) Determine the location of any maxima, minima, or saddle points for
( , ) 4 6 1f x y x y xy= + - -
(tell what each one is) 2000pq = Currently the price is $20. What will be the change of quantity sold per month if the
12. (6 pts) The demand function for a certain product is given by price changes by $5 per month?
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