# How do you find a vertical asymptote for y = sec(x)?

The vertical asymptotes of

which look like this (in red).

Let us look at some details.

In order to have a vertical asymptote, the (one-sided) limit has to go to either

So, by solving

Hence, the vertical asymptotes are

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To find the vertical asymptotes for the function y = sec(x), we need to determine the values of x for which the function approaches infinity or negative infinity.

The vertical asymptotes occur at the values of x where the function is undefined, which happens when the cosine of x is equal to zero.

Since sec(x) is the reciprocal of cos(x), it will be undefined when cos(x) is equal to zero.

The cosine function is equal to zero at x = (2n + 1)π/2, where n is an integer.

Therefore, the vertical asymptotes for y = sec(x) occur at x = (2n + 1)π/2, where n is an integer.

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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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