# For what values of x, if any, does #f(x) = 1/((x^2-4)cos(pi/2+(7pi)/x) # have vertical asymptotes?

The vertical asymptotes are given by

These are

The ad hoc graph is not to scale. graph{-1/((x^2-4)sin(21.991/x) [-3.51, 3.47, -17, 17]}

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The function f(x) has vertical asymptotes at x = 2 and x = -2.

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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.

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- Given #(u^4 + 3u + 6)^(1/2)# how do you find the limit as u approaches -2?
- How do you find the vertical asymptote of a rational function?

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