Calculate the limit as X approaches 0 of the fraction 1-cos (x) over x sin (pi x),

Question

The answer requires the replacement of the numerator and denominator with a taylor series that will produce the same limit as when lhospitals is applied to the original fraction/equation

Answer 1

Not sure if you mean that you are required to use Taylor's expansions or just compute the limit. 

 

The limit can be computed using L'Hopital's Rule twice and it turns out to be  1/(2π).