How to tell which limit is an indeterminate form?

Question

a)

b)

c)

Answer 1

The thing that'll help you the most is to simply memorize (or keep in your notes) the 7 'forms' of indeterminate limits.

To find out if a limit is in indeterminate form, you simply naively plug in the limiting value into the corresponding variable.

So for a), if you plug in 3, you get an answer of the form 0/0. This is an indeterminate form.

b) after plugging in, you get 1/0 - which is not indeterminate actually.

c) is strange, but you can still simply 'plug in' 0 from the positive side, and you can see the answer tends off towards something that looks like ln(), which is not indeterminate.

So A is the only right answer.