Originally Posted by

**masonbrewey** I need help finding two limits. I already have the answers.

Problem #1

lim .... ln(x)

x->0+ ----

.......... x

This appears to have a form of negative infinity over zero. I do not see how to simplify, or apply L'Hospital's rule.

Problem #2

lim ... x^a -a^x + a -1

x->1 ----------------

............ (x-1)^2

This has a form of 0/0, thus I apply L'Hospital's rule:

= lim ... ax^(a-1) - a^x * ln(a)

x->1 .. ------------------------

..................... 2(x-1)

and I simplify:

= lim .. ax^a - x* a^x * ln(a)

x->1 . ------------------------

.................... 2x(x-1)

The denominator goes to zero, but the numerator goes to a - a * ln(a). Again I am stuck.

Any help is appreciated.

If someone could give me a concise algorithm which would help me always find the limits(at this level of math), I would be grateful.