Question

find the taylor series generated by f=x^3 -2x+1 at a=3

Answer 1

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). :)

Answer 2

i am only familiar with the one with polynomial order? like of 4 etc...

Answer 3

OK, and what does that one look like? Could you type part of it?

Answer 4

f(a) + f(a)(x-a)... is that enough? the next one is with a factorial denominator

Answer 5

OK, that's fine.

Answer 6

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?

Answer 7

yes :)

Answer 8

oh, so that's how i determine how long the series would be. ok thanks

Answer 9

then? :)

Answer 10

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)

Answer 11

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!

Answer 12

So, can you find f' (the first derivative)?

Answer 13

3x^2 -2 ?

Answer 14

Excellent!

Answer 15

ok hey i think i got it from here. haha. thanks a lot!

Answer 16

No worries! Good luck!

Answer 17

i just follow the formula right?

Answer 18

thanks again!

Answer 19

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.

Answer 20

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). :)

Answer 21

hey i just saw this reply. haha. thanks! yeah, im starting to enjoy math more and more as i go further. thanks again!

Answer 22

thanks also for this nice info haha