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soobinkiki
Group Title
I NEED HELP.. Taylor series for x^2e^x and expanded around the point a=1/2
 one year ago
 one year ago
soobinkiki Group Title
I NEED HELP.. Taylor series for x^2e^x and expanded around the point a=1/2
 one year ago
 one year ago

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RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
Let f(x) = x^2 e^x \[f(x) = f(a) + f'(a) (xa) + \frac{f''(a)}{2!}(xa)^2+\frac{f^{(3)}(a)}{3!}(xa)^3+... +\frac{f^{(n)}(a)}{n!}(xa)^{n} +...\] So, you need to keep differentiating f(x)... Reference: http://mathworld.wolfram.com/TaylorSeries.html
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
ok i will work on it and i will put what i did
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
is f ' (x) = 2xe^x?
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
\[f'(x) = e^x \frac{d}{dx}(x^2) + x^2\frac{d}{dx}(e^x)\]
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
oh product rule
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
how many time do i have to do differentiation? (how do i know?)
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
are you there? please help me
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
what i have done so far is
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
i took differentiation of f(x)=x^2e^x
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
so i got f '(x)=x^2e^x+2xe^x f ''(x)=4xe^x+x^2e^x+2e^x
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
and i know that taylor series formula f(x)=f(a)+f'(a)(xa)+    what don't know what to do next..
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
my a = 1/2
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
should i just plug in everything on the formula?
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
so my f(a) should be 1/4e^1/2 ??
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
f(a) is right. Check this: http://www.wolframalpha.com/input/?i=+Taylor+series+x%5E2e%5Ex+at+x%3D1%2F2 It's not something nice
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
thank you RolyPoly but last quick question
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
how do i know how many times should i take differentiation of f(x)?
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
Actually, I don't know too...
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
LOLLLLLL ok! RolyPoly anyways thank you so much!
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.0
Is that (x^2)*(e^x)? @soobinkiki
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
\[f'(x) = 2xe^x+x^2e^x\]\[f''(x)=2(e^x+xe^x) + 2xe^x+x^2e^x=e^x(2+4x+x^2)\]\[f''(\frac{1}{2})=e^{\frac{1}{2}}(2+4(\frac{1}{2})+(\frac{1}{2})^2)=\sqrt{e}(2+2+\frac{1}{4}) = \frac{17}{4}\]
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
hey rolypoly can you click the website that you sent me?
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
it says f''(1/2) is 17/8(e^1/2)
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
that's why i was confused..
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
The second term is \[\frac{f''(a)}{2!}(xa)^2\]So, it is \[\frac{\frac{17}{4}\sqrt{e}}{2!}(xa)^2\]that is \[\frac{17}{8}(xa)^2\]
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
shoot...... how i missed that....
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
\[=\frac{\frac{17}{4}\sqrt{e}}{2!}(x\frac{1}{2})^2\]\[=\frac{17}{8}\sqrt{e}(x\frac{1}{2})^2\]
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
i got it now ! thanks a lot!
 one year ago

soobinkiki Group TitleBest ResponseYou've already chosen the best response.0
and the series of this problem is pretty long.......................
 one year ago

genius12 Group TitleBest ResponseYou've already chosen the best response.0
Obviously it's long, it's a series with infinite terms.. .
 one year ago
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