Tangents And The Derivative At A Point Calculating Assignment (Essay Sample)

Instructions:

30. Ball's changing volume: What is the rate of change of the volume of a ball (V=4/3 πr^3) with respect to the radius when the radius is r=2?
3.4 The Derivative as a Rate of Change
24. Marginal Revenue: Suppose that the revenue from selling x washing machines is r(x)=20,000(1-1/x) dollars.
a. Find the marginal revenue when 100 machines are produced.
b. Use the function r^' (x) to estimate the increase in revenue that will result from increasing production from 100 machines to 101 machines a week.
c. Find the limit of r^' (x) as x→∞. How would you interpret this number?

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Content:

Mathematics 1 Assignment
Question 1:
The Ball’s changing volume
V=43πr3
DVDr=4πr2
DVDrat r=2
Hence
DVDr=4π(2)2
=4π4
=16π
Question 2
Revenue rx=20,0001-1x dollars
[a.] Marginal Revenue at x=100
The rate of change of the Revenue function is the marginal revenue
Hence,
r1x=20,000/x2,
At x=100,
r1=20,000/1002
r1=20,000/10000
r1=$2
[b.] Using r1, the increase in revenue when x=101,
r1x=20,000/x2
r1 (101)=20,000/(101)2 = $1.96059
This is almost equal to wh...

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Tangents And The Derivative At A Point Calculating Assignment (Essay Sample)

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