How to calculate this?lim_(x->oo)(ln((x+2)/x)-ln((x+1)/(x-1))+1)

2 Answers
Apr 25, 2017

1

Explanation:

lim_(x->oo)(ln((x+2)/x) - ln((x+1)/(x-1)) + 1)

=lim_(x->oo)(ln(1+2/x) - ln(1+2/(x-1)) + 1)

=ln(1+0) - ln(1+0) + 1

=0-0+1

=1

Apr 25, 2017

1

Explanation:

ln((x+2)/x)-ln((x+1)/(x-1))+1 = ln((e (x + 2) (x - 1))/(x(x+1)))

and

lim_(x->oo)(ln((x+2)/x)-ln((x+1)/(x-1))+1) = lim_(x->oo)ln((e (x + 2) (x - 1))/(x(x+1)))=
= ln(lim_(x->oo)(e (x + 2) (x - 1))/(x(x+1))) =

= ln(lim_(x->oo)(e (1 + 2/x) (1 - 1/x))/((1+1/x))) = ln(e xx 1)=1