Question

Question: Estimate the limit:
lim lnx/x-1 as x goes to 1

Answer 1

do you know lhopitals rule?

Answer 2

we talked about it earlier this week in class but I didn't get a clear understanding.

Answer 3

this is LHopital's rule:
\(\huge \lim_{x\rightarrow1} \frac{lnx}{x-1}=\lim_{x\rightarrow1} \frac{[lnx]'}{[x-1]'} \)

Answer 4

ok but when he explained this it made no sense

Answer 5

prolly because of the conditions needed in order to use the rule... to use this rule you have to determine if you have an indeterminate case: 0/0, inf/inf, 0^inf, etc....

this case is 0/0, so the rule applies...

Answer 6

O ok

Answer 7

so taking the derivative of the top: 1/x
derivative of the bottom: 1

so lim(as x approaches 1) lnx/(x-1) = lim(as approaches 1) 1/x/1 = 1

Answer 8

ok