# For what values of x, if any, does #f(x) = 1/((4x+9)cos(pi/2+(4pi)/x) # have vertical asymptotes?

Asymptote is vertical at

Where

The given function:

Above function will have vertical asymptotes when denominator becomes equal to zero i.e.

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The function f(x) has vertical asymptotes at values of x where the denominator of the function becomes zero. In this case, the denominator is (4x+9)cos(pi/2+(4pi)/x). To find the values of x that make the denominator zero, we set it equal to zero and solve for x. However, it is important to note that the cosine function has a period of 2π, so we need to consider values of x that make the argument of the cosine function equal to odd multiples of π/2. Therefore, the values of x that make the denominator zero and result in vertical asymptotes are x = -9/4 and x = -9/4 + (2n+1)π/4, 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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- For what values of x, if any, does #f(x) = -tan(pi/6-x) # have vertical asymptotes?

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