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## Homework Statement

So we have just been learning limits which I understand, however there was one example which completely through me. It was regarding division by 0.

We had just been learning the known limits such as lim x->infinity (1/x) = 0 which I understood, and how anything similar such as 1/3x is 0 because its the same as 1/3 * 1/x which is basically multiplying by 0.

The problem was lim x->4+ x/(x-4), now the limit is +infinity, but I just thought it was this because 4/0 can relate to the known value of 1/x such as 4*1/0.

However the when the lecturer was explaining the proof, because the limit is for x->4+ we can't relate it to the known limits.

And the way she proved it was by letting y = x-4 (the denominator in the example) and then writing a new limit problem which was lim y->0+ (y+4)/y . The answer is still +infinity but this is the correct "proof" / logic, but I have a hard time understanding this concept.

Usually if I get stuck when I get home I just look up from other books and the net and I will find a good explanation of why, but in this case I don't even know what I am looking for, I know its to do with limits but I can't find anything similar anyway.

So if anyone could shed some light on this or perhaps this has a certain name for it...for example "solving by factorising" then I would love to know so I can start looking for the right thing.

I hope this makes sense, its the first time trying to post for help on this kind of thing.

Thanks

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