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Lo.Lee.Ta.
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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 + ...
Is this the right way to go about this?
Thanks! :)
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 + ...
Is this the right way to go about this?
Thanks! :)