Expert: Paul Klarreich - 5/5/2007

Question
The maginal cost of printing a poster when x posters have been printed is dc/dx = 1/2x^1/2 dollars. Find c(100) - c(1), the cost of printing posters 2 - 100

Answer
Questioner:   linda
Category:  Calculus
Private:  No
 
Subject:  calculus(integration)
Question:  The maginal cost of printing a poster when x posters have been printed is dc/dx = 1/2x^1/2 dollars. Find c(100) - c(1), the cost of printing posters 2 - 100
............................................  
Hi, Linda,

If all you need is the integration, that shouldn't be too bad:

*************** VIEW IN COURIER FONT ***********

Your  c(100) - c(1) is this integral:

{100
|   1/2 x^1/2 dx =
}1   
1  x^3/2
--- -----  =
2  3/2

1  2 x^3/2
--- -----  =
2  3

x^3/2
------, from x = 1 to x = 100, =
 3

1/3 [(100)^3/2 -  1^3/2] =

1/3[ 10^3 - 1^3] =

1/3[ 1000 - 1] = 1/3(999) = 333.