anonymous
  • anonymous
..
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I think the right answer to this is .12
zepdrix
  • zepdrix
So for linear approximation we use ummm...\[\large\rm f(x)\approx f(x_o)+\color{orangered}{f'(x_o)(x-x_o)}\]Something like that, ya? Where the orange stuff is our error. Wait.. is that the error? Hmmm thinking
anonymous
  • anonymous
Im not sure this problem is very confusing

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zepdrix
  • zepdrix
Yes it is +_+ So the error in the output \(\large\rm \Delta y \) ummm... ya ya ya, should be \(\large\rm f'(x_o)\color{green}{\Delta x}\), where Delta x is the distance between our base point x_o and x. \(\large\rm \Delta y\approx f'(x_o)\color{green}{(x-x_o)}\) So our base point is x=1. And we're drifting 0.001 away from that. \[\large\rm \Delta y\approx f'(1)(0.001)\]
zepdrix
  • zepdrix
Were you able to come up with a formula for Surface Area of a cube? :) And its derivative?
anonymous
  • anonymous
No I was not
zepdrix
  • zepdrix
Take a cube, call the side length x. Since it's a cube, all side lengths are the same. The area of one face will be x*x, ya? So the total surface area will be the area of all 6 panels of the cube. \(\large\rm A=6x^2\)
zepdrix
  • zepdrix
Wait wait, then how were you able to come up with .12? LOL Just straight up guessing? >.< Buhaha, Cam cam, come on!!
anonymous
  • anonymous
Haha yes it was a guess but it made sense
zepdrix
  • zepdrix
So your derivative is \(\large\rm A'=12x\). Mmm k.
zepdrix
  • zepdrix
And your error approximation for the output \(\large\rm \Delta y\) is going to be\[\large\rm =A'(x_o)\Delta x\]Our base point is x=1. And our delta is the distance between the x's, 0.001.
anonymous
  • anonymous
Ok
zepdrix
  • zepdrix
\[\large\rm =A'(1)(0.001)=?\]
anonymous
  • anonymous
1X10^-3
zepdrix
  • zepdrix
What? 0_o Plug 1 into A'(x) and then multiply that value by 0.001
anonymous
  • anonymous
Oooo .12?
zepdrix
  • zepdrix
Hmm that's not what I'm getting.. lemme see..
zepdrix
  • zepdrix
\[\large\rm =\color{orangered}{A'(1)}(0.001)=\color{orangered}{12(1)}(0.001)=12(0.001)=0.012\]
zepdrix
  • zepdrix
Is that one of our options? :o Hopefully we're doing this right <.<
anonymous
  • anonymous
Yes it is!!
anonymous
  • anonymous
Wait no its .12
zepdrix
  • zepdrix
What do the other options look like? XD
anonymous
  • anonymous
.02 .003 and none of the above
zepdrix
  • zepdrix
Hmm :p @ganeshie8 @dan815
anonymous
  • anonymous
Ill just put in .12 and hope thats the answer
anonymous
  • anonymous
Thank you for the help!
zepdrix
  • zepdrix
ya sorry :c
anonymous
  • anonymous
Its okay thanks for the help!!

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