1018
  • 1018
find the taylor series generated by f=x^3 -2x+1 at a=3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jtvatsim
  • jtvatsim
Are you familiar with the formula for Taylor series? What have you seen in class or your book? (I ask since there are different versions depending on the class). :)
1018
  • 1018
i am only familiar with the one with polynomial order? like of 4 etc...
jtvatsim
  • jtvatsim
OK, and what does that one look like? Could you type part of it?

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1018
  • 1018
f(a) + f(a)(x-a)... is that enough? the next one is with a factorial denominator
jtvatsim
  • jtvatsim
OK, that's fine.
jtvatsim
  • jtvatsim
So the equation we are using is \[f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3\] we won't need any more terms since the polynomial you have been given only goes up to the third power. Does that make sense so far?
1018
  • 1018
yes :)
1018
  • 1018
oh, so that's how i determine how long the series would be. ok thanks
1018
  • 1018
then? :)
jtvatsim
  • jtvatsim
Yes, if you didn't realize that, you could keep going but your derivatives would be 0 (the fourth derivative of an x^3 function will be zero, the fifth derivative will be zero, and so on)
jtvatsim
  • jtvatsim
Alright, so now we need: 1) To find up to the third derivative of f. That is, f', f'', and f'''. 2) We already know that a = 3. 3) Then we just plug in a = 3 into the formulas for f, f', f'', and f''' and we will be done!
jtvatsim
  • jtvatsim
So, can you find f' (the first derivative)?
1018
  • 1018
3x^2 -2 ?
jtvatsim
  • jtvatsim
Excellent!
1018
  • 1018
ok hey i think i got it from here. haha. thanks a lot!
jtvatsim
  • jtvatsim
No worries! Good luck!
1018
  • 1018
i just follow the formula right?
1018
  • 1018
thanks again!
jtvatsim
  • jtvatsim
Yep, so for example... for f'(a) you will take f'(3) which is 3(3)^2 - 2 = 27 - 2 = 25. and put that in the formula.
jtvatsim
  • jtvatsim
Good luck! You are getting to the fun part of math, where we finally figure out how calculators are able to "know" what sine, cosine and other nasty equation values are... (it's all because of Taylor Series). :)
1018
  • 1018
hey i just saw this reply. haha. thanks! yeah, im starting to enjoy math more and more as i go further. thanks again!
1018
  • 1018
thanks also for this nice info haha

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