# What is a removable discontinuity?

Please see the explanation section, below.

Recall that:

Furthermore,

(iii) the numbers in (i) and (ii) are equal.

Discontinuities in general

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A removable discontinuity, also known as a removable singularity or a removable point, is a type of discontinuity in a function where a point is missing from the graph but can be filled in or "removed" to make the function continuous at that point. This occurs when the function is undefined at a particular point, but the limit of the function as it approaches that point exists. The missing point can be filled in by assigning a value to it that makes the function continuous.

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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/((2x-3)(7x-3) # have vertical asymptotes?
- Evaluate the limit #lim_(x to pi) (e^sinx -1)/(x-pi)# without using L'Hôpital's rule?
- How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at a =-1?
- What is the limit as x approaches infinity of #cos(1/x)#?
- If limit of #f(x)=2# and #g(x)=3# as #x->c#, what the limit of #5g(x)# as #x->c#?

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