What is the limit of #(ln(x+2)-ln(x+1))# as x approaches #oo#?

Answer 1

Christopher Allers

#ln(x+2)-ln(x+1)=color(green)(0)#

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

#color(white)("XXXXXXXXXXXXX")=ln((1+2/x)/(1+1/x))#

#:. lim_(xrarroo)(ln(x+2)-ln(x+1))#

#color(white)("XXXXX")=lim_(xrarroo)ln((1+2/x)/(1+1/x))#

#color(white)("XXXXX")=ln((1+0)/(1+0))#

#color(white)("XXXXX")=ln(1)#

#color(white)("XXXXX")=0color(white)("XXXX")#since #e^0=1#

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Answer 2

Luke Alvarez

The limit of (ln(x+2)-ln(x+1)) as x approaches infinity is 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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