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Hey guys,
my question is how do you apply the binomial theorem when the quantity is raised to a non-integer value?
Specifically, (a+b)^(1/2)
I had a homework problem for my mechanics of materials class, and I got "x" far. I checked the answer, and they went further with it, calling out the Binomial Theorem as the reason for taking it a step further.
my answer was:
[1+(dL/L)]^(1/2) - 1
then their answer was (same as mine, then one step further):
1 + (1/2)(dL/L) ... - 1 "Binomial Theorem"
= (0.5*dL)/L
I don't know why this is racking my brain so hard...I think it's because of the 3 dots "..."
Thanks in Advanced
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my answer was:
[1+(dL/L)]^(1/2) - 1
then their answer was (same as mine, then one step further):
1 + (1/2)(dL/L) ... - 1 "Binomial Theorem"
= (0.5*dL)/L
Erm... that doesn't look much like the same answer to me! Your answer is:
While their answer is:
Which, if you cancel the first and last terms, gets you to their answer, plus a load of dots....?
Perhaps if you told us the original question, along with how you got to your answer, we could help you out a bit more...
Bad speling makes me [sic]
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I'm sorry, but I don't see how the square root of dL/L gives you (1/2)(dL/L)......?????
Perhaps if you told us the original question, along with how you got to your answer, we could help you out a bit more...
Perhaps...I thought my original question was sufficient enough, though.
I got as far as they did (the same way) up to the part where:
Eab = (1 + (dL/L))^(1/2) - 1
Take a look at the image (link). That's everything.
Last edited by Malik641 (2006-09-21 14:49:33)
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