My hardest and last problem about I.I. :
0 has a discontinuity here so:
to make it short, i used trigo substitution:
and im having trouble with this part
which is
i am having trouble because its indeterminate:
but i do not know how LHR works with ln
help
and thank you so much for the help on the other one
As you appear to be simply and casually stuffing in the value that you shouldn't be stuffing in, there would be no other rational conclusion other than as you have stated it. You most certainly are forgetting the rules of limits.
Rule #1: The limiting value is NOT included in the limiting process. It might not even be in the Domain! Substitution is inappropriate. Don't do it.
Rule #2: If you later find the function to be continuous at the limiting value, ignore Rule #1 and go ahead with the substitution.