QuestionQuestion

Q2) 8pts What is the average value over the interval [-1,2] for the function f(x) = 15x4 ?
Q3) 12pts Find the area between the two curves f (x) = X - 3 and g (x) = x²
Bounded by X = - 1 and X = 4
- include a sketch of the region

Q4) 15pts express answer either as fraction or to 3 decimal places ( Y .XXX)
Riemann Sum for the function f (x) = 4x³ over the interval [0, 2]
Complete the following table and evaluate the Riemann sum for f (x) when n=4:
(Fill out values as you would for a spread sheet)
a =
b =
Δx =
Recommended to use left endpoint for test point:
i    sub-region    xi    f(xi)    width      Area
1
2
3
4
Sum =

Q5) 5pts In words:
Describe what happens when the 'n' in a Riemann sum is increased?
How does this impact the answer?

Q6) 10pts
A store finds that its sales revenue changes at a rate given by:
S' (t) = - 30t² + 360t dollars per day
Where t is the number of days after an advertising campaign ends and 0 t < 28.
Find the total sales between day 5 and day 10 after the campaign ends:

Q7) 10pts A production firm measures their costs in US Dollars and has been able to quantify their marginal cost function:
Marginal Cost = 300 + 40q
Where q = quantity produced and sold daily (in units).
If it is known that the cost of producing and selling 10 units is $12000, what is the cost of producing and selling 20 units?

Q8) 10pts
Suppose that a company has a continuous income stream of f (t) = $90e3t An investor is thinking of purchasing the company, and needs to know what the present value and future value of the company are over the next In 3 years (time range 0 t In(3)). If interest rates are currently at 200%:
What is the total income?
What is the present value of the company?
What is the future value of the company?

Q9) 10pts
The demand function for a product is p = 49 - x2 and the supply function is p = 4x + 4.
Find the equilibrium point and the producer's surplus.

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