For what values of x, if any, does #f(x) = tan((7pi)/12-x) # have vertical asymptotes?
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The function f(x) = tan((7pi)/12-x) has vertical asymptotes at x = (7pi)/12 + n*pi, 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.
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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- How do you find the limit #lim (3-sqrt3^x)/(9-3^x)# as #x->2#?
- How do you find the limit of #[1/(3+x)]- (1/3) ÷ x# as x approaches 0?
- How do you find the limit of #sin((x-1)/(2+x^2)) # as x approaches infinity?

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