#A Question on Power Series

54 messages · Page 1 of 1 (latest)

unkempt valeBOT
deft anchor
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yeah

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it's kinda self intuitive

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the kth derivative

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makes the kth power of x become 1

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When naturally coeff of kth power of x is a constant now

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When u differentiate it one more time

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It becomes 0

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try doing it on a cubic polynomial

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you will get the logic

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differentiate it 4 times

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and see what happens

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See this is the power series right?

Sum(n!/(n-k)!(X^[n-k]]

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Now tell me

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N!/(N-k)! Ever be 0?

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you have over complicated things man

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just listen to me and try it on

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Ax³+bx²+cx+d

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see how many times u need to differiciate

deft anchor
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so like

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You just put 0 in there?

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yeah you evaluated the approximation about 0

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well first things first

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do you want a proof to do you just want to understand

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Okay cool

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Now see

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Answer these questions

deft anchor
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Yeah exactly

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an is also not never 0

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so overall would it be wrong to say that

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It's sometimes variable constant times x^(n-k)

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Because that defeates the whole purpose of it being a polynomial

This is an representation of a general polynomial
Like ao+a1x¹ and so no...it makes no sense for an to be zero because well they are just supposed to be any arbitrary constants

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nah chill don't worry about all that now

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would it be right to say that irs always x that is variable and the rest is the constant ≠ 0

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for it to still be a general polynomial

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And representat all a summation of all powers of x

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all the infinite series approximations you see are derived from a general polynomia

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if it works any polynomial, it works for them

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well i got college maybe I'll explain when it's over but I'll say it again, try it for a general polynomial and check

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this works because all approximations u use including the power series come from that general polynomial

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Power series is one of mathematical tools to represent any function as infinite series

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not sure why you wouldn't know that

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that's the whole purpose of infinite sums like that

deft anchor
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When u put x = 0 u approximate about that point
Here u want to calculate the kth derivative and even before u differentiated anything u plugged in the value of x which is just not even needed, I don't see the point, it makes sense both in the mind and mathematically, you could just use a general polynomial and apply the same logic it's much easier

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doesn't change anything i daid

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said

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it kinda sounds like u wanna argue more than learn

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that kinda attitude won't fly

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humble yourself

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even if you don't mean it, work on your articulation

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it's very uncivilized