For the first question, writing that may help you.
For the second one, notice that if tends to 1 from the left, then tends to 0 from the right, so that the limit you are looking for is in fact the limit of when tends to 0 from the right.
Laurent.
Thanks. I get the first one.
For the second, I'm still unclear. I notice that:
ln(1-x) = ln 1 - ln x = 0 - ln x = -ln x.
Does this help? How do I find the limit as x approaches 1 from the negative direction for -ln x?
Sorry for my clouded mind!
Jeannine
No you don't. You have ... Logarithms turns multiplications into additions (by the way, log was first introduced to simplify computations, since additions are easier).
What I suggested in my first post may be called "composition of limits". The limit of , as tends to 1 from the right, is (0, reached by upper values). And the limit of when tends to 0 from the right is . So, composing these results, the limit of when tends to 1 from the left is .
Is it clearer now?
Laurent.