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How do you find the limit of #ln ( (x+1) / x )# as x approaches infinity?

Answer 1

Aurora Alvarado

#(x+1)/x# is asymptotic to 1 when #x->infty#, so the limit must be #ln(1)=0#

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Answer 2

Emma Aldridge

To find the limit of ln((x+1)/x) as x approaches infinity, we can use the properties of logarithms and limits.

First, simplify the expression inside the logarithm by dividing the numerator and denominator by x:

ln((x+1)/x) = ln(1 + 1/x)

As x approaches infinity, 1/x approaches 0. Therefore, the expression simplifies to:

ln(1 + 0) = ln(1) = 0

Thus, the limit of ln((x+1)/x) 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.