Help with solving limits in Calculus?

Question

If you have a limit and you solve to get 0 over 0, you factor... but what if I have a number over 0? what's the procedure for such limits?

Answer 1

If you n/0 then it is undefined. There is no limit since it goes to infinity which can never be reached.

Answer 2

In evaluating limits the term with the variable approaches a constant value. if for example lim as x-->2 then 1/x--> 0.5 the variable never actually reaches the value of 2 but rather approaches it asymptotically. In the case of quotients since the numerator and the denominator approach the same value their ratio approaches 1, e.g lim k-->0 [sin k]/[tan k]-->1 even though both sin k and tan k approach 0 as k-->0. This is the reason behind differentiation [using first principles] as we consider the ratio of two infinitesimals which turns out not to be 0 and not the individual magnitudes of the numerator and denominator.

Answer 3

I'm pretty sure there is no such procedure and that it is undefined.