Question #e5299

1 Answer
Nov 6, 2017

# y = -1#

Explanation:

Evaluate:

#lim_(x->oo) (1-lnx)/(1+lnx)#

As for #x!= 1# #lnx !=0# we can divide by #lnx# the numerator and denominator:

#lim_(x->oo) (1-lnx)/(1+lnx) = lim_(x->oo) (1/lnx-1)/(1/lnx+1)#

Now, as #lim_(x->oo) lnx = +oo# then #lim_(x->oo) 1/lnx = 0# and so:

# lim_(x->oo) (1/lnx-1)/(1/lnx+1) = -1#

graph{(1-lnx)/(1+lnx) [-10, 10, -5, 5]}