Before i posted this,i tried reading my notes again and again!

so any help....id be thankful!

here is the problem...

consider f(x) = lnx, with A element in (0,1)

confirm the continuity of f in (0,1)

Let x0 be an element in (0,1)

then |lnx - lnx0| = | ln x/x0 | = ln(1 - (x0 - x)/x0)

this is smaller than or equal to 2|(x0 - x)/x0| if |(x0 - x)/x0| < 1/2

ok so first.. why is |(x0 - x)/x0| < 1/2?? did someone decide to randomnly pick 1/2...? and why is |(x0 - x)/x0| < 1/2... where did the ln go..? wouldnt it make more sense if it was .. ln|(x0 - x)/x0| < 1/2 ?

Take delta = min (epsilon*(x0)/2 , 1/2*x0)

how was delta chosen to be these??

thank you! any help ... would save me a lot of time..effort. im looking through books..online.. believe me im trying but this is logic (and i am poor at it!)

i havent written up the whole problem,only the stage i am stuck so far!