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swissgirl
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What are the first 3 terms of the Taylor expansion for the function \(f(x)=e^{2x}\)
 2 years ago
 2 years ago
swissgirl Group Title
What are the first 3 terms of the Taylor expansion for the function \(f(x)=e^{2x}\)
 2 years ago
 2 years ago

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swissgirl Group TitleBest ResponseYou've already chosen the best response.0
\(f(x)=e^{2x}\) \(f'(x)=2e^{2x}\) \(f''(x)=4e^{2x}\)
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
the taylor series is , does it say about x = 0 ? i assume it is
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
I am assuming that x=0 too
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
I am not sure why we assume x=0 in this case but whtvr
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
sum f^(n) (a) (xa)^n / n! = f(a) + f'(a) (xa) + f '' (a) (xa)^2/2! + ...
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
we dont have to, it just makes it much cleaner
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
and by cleaner i mean simpler , since x  0 = x , instead of x  1 or x  2 , etc
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
so now lets plug in f(0) + f'(0) *x + f ' ' (0) * x^2/2 + ... , since we want just the first three terms
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
So our answer wld be 1+2+2?
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
e^(2*0) + 2*e^(2*0) * x + 4*e^(2*0) *x^2/2
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
, remember a taylor series is approximating a complicated function (here exponential) with a less complicated function (polynomial)
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
1 , 2x , 4x^2/2
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
Yaaaa I think I get it
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
I get it lol just need to know how to enter it into a program. Just gotta fiddle around. THANKS
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
THANKKSSSSS :))))))))
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
Ok figured it out. Thanks for ur help
 2 years ago

perl Group TitleBest ResponseYou've already chosen the best response.1
where is my medal?
 2 years ago

swissgirl Group TitleBest ResponseYou've already chosen the best response.0
U got ur medal even b4 i got my answer :P
 2 years ago
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