anonymous
  • anonymous
I can't seem to understand what this question is asking for. Help? Use differentials to approximate the quantity. (Give your answer correct to 4 decimal places.) √10 (there's supposed to be a line over the 10 breaking the radical, which I don't know what that means.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
can you draw it with the draw button?
amistre64
  • amistre64
the OS is very jittery today :/
inkyvoyd
  • inkyvoyd
We are using the newton raphson iteration method.

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anonymous
  • anonymous
|dw:1333383058451:dw|
inkyvoyd
  • inkyvoyd
x1=x0-(f(x0)/f'(x0))
inkyvoyd
  • inkyvoyd
If this is what they want, keep looking. If it isn't, then ignore me.
experimentX
  • experimentX
(10)^(1/2) = (1+9)^(1/2) = 3(1+1/9)^(1/2) 3{1+1/2*1/9-1/2*1/2*1/2!*(1/9)^2 - 3/2*1/2*1/2*1/3!*1/9^3}
anonymous
  • anonymous
this is part of the Differentials section of my Business Calc class..
inkyvoyd
  • inkyvoyd
x1=x0-(x0^2)/(2x0)
inkyvoyd
  • inkyvoyd
|dw:1333383216015:dw|
inkyvoyd
  • inkyvoyd
|dw:1333383264595:dw|
inkyvoyd
  • inkyvoyd
|dw:1333383306978:dw|
inkyvoyd
  • inkyvoyd
I'm pretty sure this is what you are looking for, but I forget how to explain it in terms of differentials.
experimentX
  • experimentX
from binomial expansion you have: 3*(1+ 1/2*1/9 - 1/2*1/2*1/2*(1/9)^2 + 3/2*1/2*1/2*1/6*(1/9)^3) = 3.1623 which is correct up to 4 decimal places.
anonymous
  • anonymous
hmmm... Thank you experimentX, but the numerical answer you gave isn't correct according to my online homework. Inkyvoyd - its asking for a numerical value, so with your solution, do I plug in radical 10?
inkyvoyd
  • inkyvoyd
First, you take a guess for the square root of x (do 3), then iterate it until you get the first 4 digits (the first four digits don't change)
inkyvoyd
  • inkyvoyd
x(n) is thus 3, and you just keep iterating until the digits do not change for the first 4 numbers (or the first n numbers, depening on how many you need)
inkyvoyd
  • inkyvoyd
btw, th left side is x(n+1), and all the x's on the right side are x(n)s. sorry bout that.
experimentX
  • experimentX
what is your answer??
inkyvoyd
  • inkyvoyd
The square root of ten to 4 digits is what they are looking for.
inkyvoyd
  • inkyvoyd
You can use any numerical method you want (or, like me, a calculator), but what I showed you before was what they were looking for.
inkyvoyd
  • inkyvoyd
If you don't understand the method very well, (I don't either xD), you can read up on it on wikipedia, http://en.wikipedia.org/wiki/Newton%27s_method But, what they are asking for is probably the square root of 10.
anonymous
  • anonymous
experimentX - the homework doesn't give me the correct answer, I just get unlimited tries to get the correct one (check mark)
anonymous
  • anonymous
yeah, i tried square root of 10, and it doesn't accept it. I don't know what it's specifically asking. Maybe I should email the professor.
inkyvoyd
  • inkyvoyd
Yes, I'm probably wrong (I "self-studied"calculus). You sure you havn't rounded?
anonymous
  • anonymous
i rounded, too.. tried 3.1623, 3.1622, 3.1620.. the problem had a second example: square root of 37, and when I entered it on the calculator (6.0823) it accepted it. Maybe its an error on the online hw's part.
inkyvoyd
  • inkyvoyd
Maybe it is 0.o. You understand the iteration/differential method though, right?
inkyvoyd
  • inkyvoyd
well, sorry, but I have to sleep lol. Good luck (it's probably homework error)
anonymous
  • anonymous
yes, kind of.. thank you for your help!

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