What is the limit as x turns to infinity of #x(ln(x+3)-ln(x-3))#?

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Answer 1 · 2018-05-11T14:21:32

#lim_(x->oo)x(ln(x+3)-ln(x-3))=1#

#lim_(x->oo)x(ln(x+3)-ln(x-3))#

= #lim_(x->oo)xln((x+3)/(x-3))#

= #lim_(x->oo)xln(1+6/(x-3))#

= #lim_(x->oo)ln(1+6/(x-3))^x#

= #lim_(x->oo)ln[(1+6/(x-3))^((x-3)/6)]^((6x)/(x-3))#

= #lim_(x->oo)ln[(1+6/(x-3))^((x-3)/6)]^(6+18/(x-3))#

= #1^6#

= #1#