What I am trying to get at is the sort of initial assessment of a function, or in other words, the line of reasoning employed before any calculations, that leads to the conclusion that an asymptote of such and such a kind is present.
From what I gather, an asymptote is a value which the function never reaches, it only “approaches” it. But the connection between this idea and a mathematical expression is veiled in darkness, so likewise are the procedures—although I can perform them.
I apologize for the perhaps broad or vague question. My ignorance is such that I cannot see exactly what it is that confuses me, and so I cannot formulate a more precise question.
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Usually you look for singularities, or places where the function either goes to infinity or infinitely small.
A good example is if you see something like 1/x , as x gets closer and closer to zero, the value of 1/x just keeps getting bigger and bigger, approaching infinity.
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