How do you find the limit of #ln x * tan^-1(x)# as x approaches infinity?

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Answer 1 · 2018-06-19T08:14:13

#lim_(x->oo) lnx arctanx = +oo#

We know that:

#lim_(x->oo) arctan x = pi/2#

while:

#lim_(x->oo) lnx = +oo#

It follows that:

#lim_(x->oo) lnx arctanx = +oo#

graph{lnx arctanx [-10, 10, -5, 5]}