## Question

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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