also how is it that yet which equals 1/0 which is undefined, I think these problems are of the same vein.
i've also noticed on some calculators the sin of 0 gives me a really small number instead of 0.
"explanation" leaves a bit to be desired ...
saying it w/o using the oft misused word "infinity" ...
as , the first term becomes a very large, unbounded positive value
as , the second term becomes a very large, unbounded negative value
(large, unbounded positive value) + (large, unbounded negative value) is an indeterminate value ... hence the need to set up the limit ao L'Hopital can be used.