How do you find the Limit of #ln[(R-3)/(R-2)] # as R approaches infinity?

Answer 1

Ezekiel Alexander

#lim_(R->oo) ln((R-3)/(R-2)) =0#

Dividing numerator and denominator of the rational function by #R# you have:

#lim_(R->oo) ln((R-3)/(R-2)) = lim_(R->oo) ln((1-3/R)/(1-2/R))=ln1 = 0#

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Answer 2

Ezra Adams

To find the limit of ln[(R-3)/(R-2)] as R approaches infinity, we can use the properties of logarithms and limits.

First, let's simplify the expression inside the natural logarithm.

(R-3)/(R-2) can be rewritten as 1 - 1/(R-2).

Now, as R approaches infinity, 1/(R-2) approaches 0.

Therefore, the expression simplifies to 1 - 0, which is equal to 1.

Taking the natural logarithm of 1 gives us ln(1) = 0.

Hence, the limit of ln[(R-3)/(R-2)] as R 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.