# Find Taylor series generated by e^x centered at 0.

1. Apr 15, 2013

### Lo.Lee.Ta.

1.
a. Find Taylor series generated by ex2 centered at 0.

b. Express ∫ex2dx as a Taylor series.

2. For part a, I just put the value of "x2" in place of x in the general form for the e^x Taylor series:

ex: 1 + x + x2/2! + x3/3! + ...

ex2: 1 + x2 + x4/2! + x6/3! + ...

For part b, I just took the integral of the Taylor series for ex2:

= 0 + 2x + 1/2*4x3 + 1/6*6x5 + ...

= 2x + 2x3 + x5 + ...

Thanks! :)

2. Apr 15, 2013

### tiny-tim

HI Lo.Lee.Ta.!

a. looks fine
Looks like the derivative to me

3. Apr 15, 2013

### Lo.Lee.Ta.

#O_O AGH! I did take the derivative! Thanks! ha

So, it should be: x + 1/3(x3) + 1/10(x5) + 1/42(x7) + ...

Is this right?

Thanks! :)

4. Apr 15, 2013

### Staff: Mentor

Don't forget the constant of integration ... Otherwise, it looks fine.