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Find the Taylor polynomial T3(x) for the function f(x)=1/x centered at the number a=4?
I feel like I'm doing it right but I keep getting the wrong answer, can someone please work this out so I can see if it's the website or if it's me? (the site has glitched before to make right answers wrong).
2 Answers
- RaffaeleLv 79 years agoFavorite Answer
f(x) = 1/x = x^(-1)
f'(x) = - x^(-2)
f''(x) = 2x^(-3)
f'''(x) = - 6 x^(-4)
f(4)=1/4
f'(4)=-1/16
f''(4)= 1/32
f'''(4) = - 1/1536
f(x) = f(4) + f'(4)(x - 4) + f''(4)(x - 4)^2/2 + f'''(4)(x - 4)^3/(3*2)
f(x) = 1/4 - (x - 4)/16 + (x - 4)^2/64 - (x - 4)^3/256
- CastigatorLv 49 years ago
the third term would be :
f ' ' ' (4) / 4! * ( x - 4 )^3 / 3 !
f ' ' ' (4) = -3 / 128
