Question

Please help me with calc 2 material

Answer 1

How would I go about finding the Taylor series for:\[f(x) = \int\limits_{0}^{x}((e^t -1)/t) dt\]where a=0?

Answer 2

Daaawg, hit us up with that problem.

Answer 3

Find derivatives of the integrand

Answer 4

Taylor series is:
f(a) + f'(a) * (x-a) + (f''(a) * (x-a)^2)/2 + (f'''(a) * (x-a)^3)/(3!)...

Answer 5

I think the derivative of integrand is:\[(te^t-e^t+1)/t^2\]im not sure what to do next

Answer 6

Do you know where you Taylor Series should be centered at, If not specified ceter it at 1

Answer 7

Centered? It gave 0.

Answer 8

I am still not sure what to do next

Answer 9

Master, isn't it true that the integral of that function is the antideriative of that function? So what do you get if you take the derivative of the antiderivative?

Answer 10

The original function?

Answer 11

Awww dang. You right.

Answer 12

So that's your first derivative. Evaluate at 0 to get f'(a). Multiply that by (x-a) =x. That gives you the second term of the Taylor series.

Answer 13

Thanks!

Answer 14

My pleasure =)