Using differentials to estimate the maximum possible error

  • #1

Homework Statement


Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of the box.

Homework Equations


Volume of the box = [x][/2] * [y][/2] , x base side, y height

The Attempt at a Solution


▽f(x,y) = x^2y + 2xy , x^2 * ((1+y))

and i am unsure of how i can move on from here! do i sub in the x and y values 3 and 5? or the error 0.02 and 0.01 respectively?

thank you![/B]
 

Answers and Replies

  • #2
vela
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Homework Statement


Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of the box.

Homework Equations


Volume of the box = [x][/2] * [y][/2] , x base side, y height
What does this mean?

The Attempt at a Solution


▽f(x,y) = x^2y + 2xy , x^2 * ((1+y))
Not sure what you've done here either.

You want to express the differential df in terms of dx and dy.

and i am unsure of how i can move on from here! do i sub in the x and y values 3 and 5? or the error 0.02 and 0.01 respectively?

thank you![/B]
 
  • #3
34,687
6,394

Homework Statement


Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of the box.

Homework Equations


Volume of the box = [x][/2] * [y][/2] , x base side, y height
I'm as mystified as vela is by what you have here. It's given that the box has a square base. The volume of a rectangular box is the area of the base times the height.
whatphysics said:

The Attempt at a Solution


▽f(x,y) = x^2y + 2xy , x^2 * ((1+y))[/B]
???
Where does this come from?
You don't want the gradient -- you want the differential of the volume, dV.
whatphysics said:
and i am unsure of how i can move on from here! do i sub in the x and y values 3 and 5? or the error 0.02 and 0.01 respectively?
 

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