# What is the discontinuity of the function #f(x) = |x-5|/(x-5)# ?

There is a jump discontinuity at

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The function f(x) = |x-5|/(x-5) has a discontinuity at x = 5.

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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.

- For what values of x, if any, does #f(x) = 1/((x-3)(x+4)(e^x-x)) # have vertical asymptotes?
- How do you find the limit of #(sqrt(x+5)-3)/(x-4)# as #x->4#?
- How do you find the limit of #(x^2-3x+2)/(x^3-4x)# as x approaches 2 from the right, as x approaches -2 from the right, as x approaches 0 from the left, and as x approaches 1 from the right?
- How do you use the epsilon delta definition of limit to prove that #lim_(x->1)(x+2)= 3# ?
- What is the limit of #(sqrt(x^2+4x+1)-x) # as x goes to infinity?

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