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



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swissgirl
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\(f(x)=e^{2x}\)
\(f'(x)=2e^{2x}\)
\(f''(x)=4e^{2x}\)

perl
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the taylor series is , does it say about x = 0 ? i assume it is

swissgirl
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I am assuming that x=0 too

swissgirl
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I am not sure why we assume x=0 in this case but whtvr

perl
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sum f^(n) (a) (xa)^n / n!
= f(a) + f'(a) (xa) + f '' (a) (xa)^2/2! + ...

perl
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we dont have to, it just makes it much cleaner

perl
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and by cleaner i mean simpler , since x  0 = x , instead of x  1 or x  2 , etc

perl
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so now lets plug in
f(0) + f'(0) *x + f ' ' (0) * x^2/2 + ... , since we want just the first three terms

swissgirl
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So our answer wld be 1+2+2?

perl
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e^(2*0) + 2*e^(2*0) * x + 4*e^(2*0) *x^2/2

perl
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, remember a taylor series is approximating a complicated function (here exponential) with a less complicated function (polynomial)

perl
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1 , 2x , 4x^2/2

perl
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ok?

swissgirl
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Yaaaa I think I get it

swissgirl
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I get it lol just need to know how to enter it into a program. Just gotta fiddle around. THANKS

swissgirl
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THANKKSSSSS :))))))))

swissgirl
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Ok figured it out. Thanks for ur help

perl
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:D

perl
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where is my medal?

perl
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thanks

swissgirl
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U got ur medal even b4 i got my answer :P