Find limit, x->1, (ln(4x)-ln(4))/ln(x), x->infty, (1-e^x)/(1

[harvez_007]

Hi

I am currently trying to get my head around limits involving logarithms and exponentials.

These are the two equations i am stuck on:

lim (ln(4x) - ln(4)) / (ln(x))
x->1

lim (1-e^x) / (1+2e^x)
x->?

Could you please show working that would be greatly appreciated.

Cheers, Harvez.

 

[skeeter]

Re: Finding the limit of these equations:

Hi

I am currently trying to get my head around limits involving logarithms and exponentials.

These are the two equations i am stuck on:

lim (ln(4x) - ln(4)) / (ln(x))
x->1

start by using the properties of logs to simplify the numerator ... the limit will be rather obvious after that

lim (1-e^x) / (1+2e^x)
x->?

divide every term by e[sup:2xdrikiw]x[/sup:2xdrikiw], then take the limit