Question #07d97

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Answer 1 · 2018-01-21T08:27:26

#-0.307#

You now have #lim_(xrarr1)ln((x+1)/(x-1))#

Directly inputting for #x# will not work, as you will be required to solve #2/0#, an impossible feat.

Remember the laws of logarithms, that can be applied to natural logs: #ln(a/b)=lna-lnb#.

So now:

#lim_(xrarr1)ln(x+1)-ln(x-1)#

Now you can input the values:

#ln(1+1)-ln(1-1)#

#ln2-ln0#
But wait! #ln 0# is undefined! So #ln((x+1)/(x-1))# is undefined at #x=1#.

So the answer is infinity.