log and exponential questions
These aren't too hard... they are just some problems that Im not quite sure on. If you can help for each I really would appreciate it..
The first one is...
Find the limit as x goes to infinity for ( (e^3x)-(e^-3x) ) / ( (e^3x)+(e^-3x) )
now i know you are supposed to divide num and denom by e^3x to =
lim x -> oo ( 1-(3^-6x) ) / ( 1+(e^-6x) )
which is basically one minus infinity over 1 plus infinity..
The answer of course, is -1... how do i reason that? Im confused there...
Second question is, Differentiate Log10(x/(x-1))
The first thing i did to make myself confused is thinking that log base 10 x is = lnx.. What is the real relationship? I forgot... and the second thing, could I change the function to f(x) = log base 10 x - log base 10 (x-1) and then differentiate from there?
And the last question is to evaluate the integral of Log base 10 x over x dx
(sorry for having to say it in words)
For this one, the book says something about changing it to lnx/ln10/x... i think... do you have to do it this way?
Thank you for your help