# For what values of x, if any, does #f(x) = 1/((5x+8)cos(pi/2-(12pi)/x) # have vertical asymptotes?

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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 (5x+8)cos(pi/2-(12pi)/x). To find the values of x that make the denominator zero, we need to solve the equation (5x+8)cos(pi/2-(12pi)/x) = 0. However, the cosine function is never equal to zero, so there are no values of x that make the denominator zero. Therefore, the function f(x) does not have any vertical asymptotes.

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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 the limit of # (tan2x)/(5x)# as x approaches 0?
- How do you find the limit of #2sin(x-1)# as x approaches 0?
- How do you find the limit of #(2x+1)^4/(3x^2+1)^2# as #x->oo#?
- How do you find the limit of #(sqrt(x+6)-x)/(x^3-3x^2)# as #x->-oo#?
- What is the limit of #(3x^2+20x)/(4x^2+9)# as x goes to infinity?

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