# What does the vertical asymptote represent?

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The vertical asymptote represents a vertical line on a graph that the function approaches but never crosses. It occurs when the function approaches infinity or negative infinity as the input approaches a certain value.

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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.

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.

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.

- How do you find #lim cost/t^2# as #t->oo#?
- How do you determine the limit of #1/(x-3)# as x approaches #3^+#?
- How does the vertical asymptotes affect limits at infinity?
- For a given function #f(x)=x^a/x^b#, is it correct to say that #f(0)=0,1or"undefined"# depending on the values of #a# and #b#?
- What is the limit of # (x^2 − 5x)/(x^2 − 4x − 5)# as x approaches 5?

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