Question

What is the value of f^(10)*3 , the tenth derivative of f at x=3. I will write the series with the equation box.

Answer 1

\[\sum_{k=0}^{\infty} (1/2) ^k * [(x-3)^k/ k!)]\]

Answer 2

Let T(x)be the Taylor series for a fucntion f. What is the value of f^10 *3, the tenth derivative of f at x=3?

Answer 3

@amistre64 can u help

Answer 4

has my icon been on all night?

Answer 5

this is just C (x-3)^k when we clean it up

Answer 6

(x-3)^k goes:

1: k (...)^(k-1)
2: k(k-1) (...)^(k-2)
3:k(k-1)(k-2) (...)^(k-3)

n: k(k-1)(k-2)...(k-(n-1)) (...)^(k-n)

for the powers that drop in front and the powers that subtract down the derivatives

Answer 7

the only issue I see might be when k-some value r = -1 and we derive it ....

Answer 8

nah, thats only with integrating :)

Answer 9

\[\sum_{k=0}^{\infty} \frac{(1/2) ^k}{k!} (\color{red}{K})(x-3)^{k-10}\]

Answer 10

where the red K is think might be k! .. but id have to think it out :)

Answer 11

since we drop down to (k-9); everything up to that point goes zero til k=9 so we might as well start it out at k=10

\[\sum_{k=10}^{\infty} \frac{(1/2) ^k}{k!} (\color{red}{K})(x-3)^{k-10}\]

then its really just defining k! at that point isnt it.

10.9.8.7.6.5.4.3.2.1 .... so it cancels with k! in the denom and it all goes away in my view.

\[\sum_{k=10}^{\infty} \frac{(1/2) ^k}{\cancel{k!}} (\color{red}{\cancel{k!}})(x-3)^{k-10}\]

\[f^{(10)}(x)=\sum_{k=10}^{\infty} (\frac{1}{2})^k(x-3)^{k-10}\]

Answer 12

so after all that work :) when we input x=3 we get 3-3=0 and it all goes to zero

Answer 13

or its undefined since 0^0 is undefined

Answer 14

http://www.wolframalpha.com/input/?i=10th+derivative+e%5E%28%28x-3%29%2F2%29

the original summation leads to e^((x-3)/2) and the 10th derivative of that is the wolfs doing: 1/1024 so either ive messed it up someplace, or entered it wrong in the wolf .. and possibly both