Quandaries and Queries


Hi, I would like to see the Maclaurin series generated by
f(x)=x3·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?


Latto, student.



Hi Latto,

There is a theorem in calculus that states

If f(x) = c0 + c1(x - a) + c2(x - a)2 + ··· + cn(x - a)n+ ··· for all x in some interval containing a, then the series is the Taylor series for f about a.

What this means is that if you can construct a series representation for the function you have that converges in an interval containing 0, then it is the Maclaurin series.

For you example take the Maclaurin series representation of cos(x), multiply each term by x3, and then add 1.



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