Subject: calculus question

The limit of the following as x goes to infinity is 2*y. Y is a constant.

lim 2*x*log(x/(x-y)) = 2*y

I don't understand, though, how this answer is arrived at. Can you help?


Hi Dan,

As x goes to infinity x/(x-y) approaches 1 and hence log(x/(x-y)) approaches log(1) = 0. Thus as x goes to infinite your limit approaches infinity times zero, which makes it a candidate for l'Hospital's Rule.

To put the limit into the form of "0/0" write

Now apply l'Hospital's Rule.

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