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i must find the the Taylor series expansion (i've been asked not necessarily calculating it directly) and the convergence radios for this function :

$$f(x) = \int_0^x \cos(\sqrt{t}\ ) \, dt$$

I am new to this field, and im not really sure what do i need to do, so maybe this is an elementary question, but i'd appreciate it if you add explanations so i can understand.

Thanks alot.

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Hint: to find the Taylor series expansion for this function, find the Taylor series expansion for $\cos(\sqrt{t})$, and then integrate it from $0$ to $x$.

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    $\begingroup$ If I'm not mistaken, the radius of convergence will not change when you integrate. $\endgroup$ Jun 7 '13 at 19:14
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    $\begingroup$ That's what I was thinking, @MichaelHardy, but I wasn't positive. Edit: this indeed seems to be the case. scipp.ucsc.edu/~haber/ph116A/powertheorems.pdf $\endgroup$ Jun 7 '13 at 19:14
  • $\begingroup$ @AWertheim i was said that i dont have to calculate the Tayolr series expansion directly.. can you explane what that means? in addition, if i would of calculate the talyor series... around what point do i calculate it? $\endgroup$
    – Simba
    Jun 8 '13 at 8:48

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