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What are the first 3 terms of the Taylor expansion for the function \(f(x)=e^{2x}\)
 one year ago
 one year ago
What are the first 3 terms of the Taylor expansion for the function \(f(x)=e^{2x}\)
 one year ago
 one year ago

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swissgirlBest ResponseYou've already chosen the best response.0
\(f(x)=e^{2x}\) \(f'(x)=2e^{2x}\) \(f''(x)=4e^{2x}\)
 one year ago

perlBest ResponseYou've already chosen the best response.1
the taylor series is , does it say about x = 0 ? i assume it is
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
I am assuming that x=0 too
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
I am not sure why we assume x=0 in this case but whtvr
 one year ago

perlBest 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! + ...
 one year ago

perlBest ResponseYou've already chosen the best response.1
we dont have to, it just makes it much cleaner
 one year ago

perlBest 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
 one year ago

perlBest 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
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
So our answer wld be 1+2+2?
 one year ago

perlBest ResponseYou've already chosen the best response.1
e^(2*0) + 2*e^(2*0) * x + 4*e^(2*0) *x^2/2
 one year ago

perlBest 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)
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
Yaaaa I think I get it
 one year ago

swissgirlBest 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
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
THANKKSSSSS :))))))))
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
Ok figured it out. Thanks for ur help
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
U got ur medal even b4 i got my answer :P
 one year ago
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