Question

consider a closed rectangular box with a square base, whose edges have length x. If x is measured with error at most 2% and the height y is measured with error at most 3%, use a differential to estimate the corresponding %error in computing the box's surface area.

Answer 1

how much of an estimate can we make? I used x+dx, y+dy and found a term for the error, but it doesnt exactly come out nice.

Answer 2

the answer should be +/- 5%

Answer 3

ok I got about 4%

Answer 4

here is my attempt, given: dx/x=2%, dy/y=3%, and i am looking for ds/s

Answer 5

using partial derivatives, ds=(4x+4y)dx+(4x)dy

Answer 6

ds/s=(4x+4y)dx+(4x)dy /(2x^2+4xy), and then i am stuck.. i was able to get dx/x but not dy/y

Answer 7

k give me a sec to think about this

Answer 8

Thanks so much!!!!

Answer 9

k it turns out the same way as the way I did it actually:

multiply the first part of the numerator by x/x and the second part by y/y

then you have ((4x^2+4xy)dx/x+4xy(dy/y)) we know dx/x=.02, dy/y=.03

pluging in

(.08x^2+.08xy+.12xy)/(2x^2+4xy)

=(.08x^2+.2xy)/(2x^2+4xy)

now here is why I asked how big of an estimate we can make, we round .08 to .1 so that it comes out nicely:

.1(x^2+2xy)/(2(x^2+2xy))=.1/2=.05

5%

Answer 10

AWESOME! i got stuck because i didn't round it off.......

Answer 11

yeah it's not nice, but they just want an estimate so I geuss it is ok

Answer 12

Thank you very much :)

Answer 13

you're welcome :)