Why can't you just substitute ?
You should know that and .
As long as the denominator is not 0, taking the limit of each part separately is just using the various "laws of limits" and is valid. If each part is a continuous function (and the denominator is not 0 so the whole combination is a continous function) then that is exactly the same as "substitute ".
Can someone tell me how to solve these kind of problems? I have a couple of these in my homework, and had one on a quiz today but couldn't really figure out how to solve them
1)
lim sin4x/9x
x->0
2)
lim
x->0 tan4x/2x
I tried to put it into wolfram alpha but that used the L'Hopital's rule which made no sense to me since the professor didn't teach L'Hopital's rule to my class