Exercise. For the denominator, the sum of the first three nonzero terms in the Taylor series centered at a = 0 is: 2z sin ( ) = p/1!x+0/2!x*2+ X I + I' + Exercise. Note that we may need more terms, but we can always exhibit more if necessary. Step 2: Now that we have the series, let's substitute them into the limit: +p'+... 1 lim = lim 140 2x sin (?) +wally... Step 3: We can proceed by factoring out the dominant terms from the numerator and denominator: As r -+ 0, the dominant power of z in the numerator is r As r -+ 0, the dominant power of z in the denominator is r