(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to find the radius of convergence for each: (A) e^3x (B) xe^(-x)^2 (C) (e^x-1)/x

2. Relevant equations

So I used the ratio test for each. I'll only write out the answer I got since I'm pretty sure I did them correctly.

(A) abs. value (x) lim n--> infinity 3/(n+1)

(B) abs. value (x^2) lim n--> infinity 1/(n+1)

(C) abs. value (x) lim n--> infinity 1/(n+1)

3. The attempt at a solution

My question isn't so much about how to do them (I can always go back and redo the ratio test if my answers are wrong) but about what to claim as the radius of convergence. For all of these, it seems to be infinity, and I know e^x has a radius of convergence of infinity. Do all of these really have the same radius of convergence?

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# Radii of convergence for exponential functions

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