swissgirl
  • swissgirl
What are the first 3 terms of the Taylor expansion for the function \(f(x)=e^{2x}\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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swissgirl
  • swissgirl
\(f(x)=e^{2x}\) \(f'(x)=2e^{2x}\) \(f''(x)=4e^{2x}\)
perl
  • perl
the taylor series is , does it say about x = 0 ? i assume it is
swissgirl
  • swissgirl
I am assuming that x=0 too

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swissgirl
  • swissgirl
I am not sure why we assume x=0 in this case but whtvr
perl
  • perl
sum f^(n) (a) (x-a)^n / n! = f(a) + f'(a) (x-a) + f '' (a) (x-a)^2/2! + ...
perl
  • perl
we dont have to, it just makes it much cleaner
perl
  • perl
and by cleaner i mean simpler , since x - 0 = x , instead of x - 1 or x - 2 , etc
perl
  • perl
so now lets plug in f(0) + f'(0) *x + f ' ' (0) * x^2/2 + ... , since we want just the first three terms
swissgirl
  • swissgirl
So our answer wld be 1+2+2?
perl
  • perl
e^(2*0) + 2*e^(2*0) * x + 4*e^(2*0) *x^2/2
perl
  • perl
, remember a taylor series is approximating a complicated function (here exponential) with a less complicated function (polynomial)
perl
  • perl
1 , 2x , 4x^2/2
perl
  • perl
ok?
swissgirl
  • swissgirl
Yaaaa I think I get it
swissgirl
  • swissgirl
I get it lol just need to know how to enter it into a program. Just gotta fiddle around. THANKS
swissgirl
  • swissgirl
THANKKSSSSS :))))))))
swissgirl
  • swissgirl
Ok figured it out. Thanks for ur help
perl
  • perl
:D
perl
  • perl
where is my medal?
perl
  • perl
thanks
swissgirl
  • swissgirl
U got ur medal even b4 i got my answer :P

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