anonymous 4 years ago lim as x approaches 0 for f(x)=ln(x/(x-1)

1. TuringTest

$\frac{\ln x}{x-1}$??

2. anonymous

not quite, natural log of the entire fraction

3. TuringTest

$f(x)=\ln(\frac x{x-1})$yes?

4. anonymous

yep

-ininity

6. anonymous

how did you get that?

7. TuringTest

long division$\ln(1+\frac1{x-1})$x goes to zero and we get$\ln(1+(-1))=\ln 0=-\infty$

ln is continous, so lim and ln can change places, so when you do that, and than plug in x=0 you get ln0 which is the result turing test wrote

9. anonymous

ok that makes sense. Thank you

you're welcome :D

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