I've just started working with Taylor series and can't figure out how to find the series of the following function:

g(x)=$\displaystyle \int_0^x [2e^v+3e^{-v}] dv$

about x=0

Could anyone please show me the solution?

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- Dec 14th 2010, 09:30 AMgoblinfHelp solving taylor series.
I've just started working with Taylor series and can't figure out how to find the series of the following function:

g(x)=$\displaystyle \int_0^x [2e^v+3e^{-v}] dv$

about x=0

Could anyone please show me the solution? - Dec 14th 2010, 09:39 AMtonio
- Dec 14th 2010, 09:59 AMgoblinf
And for which values of x does the series converge?

- Dec 14th 2010, 11:32 AMTheCoffeeMachine
- Dec 15th 2010, 01:29 AMgoblinf
- Dec 15th 2010, 01:31 AMProve It
It's well known that the Taylor series for $\displaystyle \displaystyle e^x$ is convergent for all $\displaystyle \displaystyle x$.

But this is also relatively easy to show using the ratio test.