I am trying to sketch the curve y=x+1/x
Following are the steps that are generally followed. But I don’t understand one thing
First I note that while as x tends to infinity, 1/x tends to 0. Then we conclude that y tends x, since 1/x tends to 0. The thing that I don’t understand is if x tends to infinity, so why don't we say y tends to infinity too.

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y = (x+1)/x ? or y = x + (1/x)

No as it is

I mean using the math rule

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