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12:29 AM on 11/16/09 
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concernedparent
I'm very concerned.
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San Jose, CA
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This is sorta urgent! Since I have my quiz tomorrow and I can't for the life of me figure out this topic. My teacher didn't even cover it in class, just said it would be on the quiz.
02:32 AM on 11/16/09 
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tonyC4L
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Lake Forest, CA
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Could someone explain how to find the second order taylor polynomial for a multivariable function? For example:

f(x, y) = 2/(x^2 + y^2 + 2), at a = (0,0)
Hmm I don't really remember this but this is what I've found with a little research:

For any function f(x,y), the Taylor series to second order about the point (a,b) is given by



Using that you should be able to plug in with your specific f about (0,0).

this was just from wikipedia btw: http://en.wikipedia.org/wiki/Taylor_... ral_variables
sorry I can't be much more help than that.
08:35 AM on 11/16/09 
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concernedparent
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San Jose, CA
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Actually that does help clarify something definitely. For some reasons I didn't see that on Wikipedia..haha. thanks.
09:13 AM on 11/16/09 
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Rowoverdramatic
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I have some stuff I need help with before my mock exam tomorrow, but it'll be pathetically easy to you guys. =/
11:25 AM on 11/16/09 
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John JD Dorian
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St Louis, MO
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I have some stuff I need help with before my mock exam tomorrow, but it'll be pathetically easy to you guys. =/

we enjoy it anyway.
11:32 AM on 11/16/09 
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John JD Dorian
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Very nice, thank you. We actually have not learned the definition of continuity yet in my class, so I didn't make that connection when taking the test, but after reading the definition and then your proof it all makes sense.

the whole thing is pretty straightforward, with one interesting kink. in the case where x is irrational, at first i just tried to pick a rational y out of the interval (x-d, x+d), but then i realized that i didn't necessarily have my result, so i actually had to restrict myself to (x, x+d). then when i was writing it up i realized that x might be negative in which case to get |y| > |x| i would actually have to choose a y out of (x-d, x), so there are really two cases.

of course, it's probably easier to just to do it all in one case and say pick a y out of (x-d, x+d) such that |y| > |x|, but i find it nicer to flush things out a bit.

anyway, that's what i found a tad interesting.
06:00 PM on 11/16/09 
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geebee889
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Woodstock, GA
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I will most likely post in here later tonight...I still have my math to do.
07:30 PM on 11/16/09 
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John JD Dorian
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I will most likely post in here later tonight...I still have my math to do.

bring it.
07:50 PM on 11/16/09 
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geebee889
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Okay, we're doing logarithms and natural logs. I understand how to convert equations and solve for them, but finding the differentiating is where I get confused.

Y = x^6 lnx - (1/4)x^4

or

Y = ln (7x^2 +5x +2)
08:17 PM on 11/16/09 
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John JD Dorian
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St Louis, MO
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Okay, we're doing logarithms and natural logs. I understand how to convert equations and solve for them, but finding the differentiating is where I get confused.

Y = x^6 lnx - (1/4)x^4

or

Y = ln (7x^2 +5x +2)

do you mean finding the derivative?
09:06 PM on 11/16/09 
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John JD Dorian
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St Louis, MO
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When taking derivatives of lns/logs just say this in your mind. "The log of crap is: 1 over crap, times the derivative of crap."

that's true for log base e (ln). if it's log base something else, there's an extra term in there.
10:48 PM on 11/16/09 
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concernedparent
I'm very concerned.
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San Jose, CA
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I only wrote "logs" so it would read better. I always assume people are working in base e unless otherwise stated.
Math fight!
10:57 PM on 11/16/09 
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tonyC4L
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Lake Forest, CA
Male - 26 Years Old
I pretty much always write log for base e. What really tripped me up was the use of Log vs log in my complex analysis book. I don't know if that's an author thing or if math people actually use a capital L for the principal branch but it took me a while to get the hang of it. Mostly because my teacher didn't tell us about the difference and used them interchangeably (and still does... students are always correcting him in lecture).
03:39 AM on 11/17/09 
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geebee889
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Woodstock, GA
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do you mean finding the derivative?

When taking derivatives of lns/logs just say this in your mind. "The log of crap is: 1 over crap, times the derivative of crap."

that's true for log base e (ln). if it's log base something else, there's an extra term in there.


Yeah, I meant the derivative. Is it always like that for ln?
06:10 AM on 11/17/09 
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John JD Dorian
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St Louis, MO
Male - 25 Years Old
I only wrote "logs" so it would read better. I always assume people are working in base e unless otherwise stated.

often in very elementary texts log is used as base 10 and ln as base e, so i wanted to make sure the one with the question wasn't confused.

but yes, among mathematical sophisticates, log is always assumed to be base e, because of course the very definition of log(x) is the integral from 1 to x of dt/t.



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