# What are the removable and non-removable discontinuities, if any, of #f(x)=abs(x-9)/ (x-9)#?

There's a non-removable discontinuity in

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The function f(x) = abs(x-9)/ (x-9) has a removable discontinuity at x = 9. There are no non-removable discontinuities.

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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 evaluate the limit #(x^2-9)/(x^3-27)# as x approaches #3#?
- For what values of x, if any, does #f(x) = 1/((12x+3)sin(pi+(6pi)/x) # have vertical asymptotes?
- How do you find the Limit of #ln(ln(x))/x# as x approaches infinity?
- How do you evaluate the limit #(6x+1)/(2x+5)# as x approaches #oo#?
- For what values of x, if any, does #f(x) = -tan(pi/6-x) # have vertical asymptotes?

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