# What is the definition of continuity at a point?

Definition

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Continuity at a point refers to a property of a function where the function is defined and has a limit at that specific point, and the limit is equal to the value of the function at that point. In other words, a function is continuous at a point if the function is defined at that point, the limit of the function as it approaches that point exists, and the limit is equal to the value of the function at that point.

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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 #x-sqrt(x^2+3x)# as x approaches negative infinity?
- How do you the limit of a piecewise function?
- How do you find the Limit of #[(sin x)(sin 2x)] / (1 - cos x) # as x approaches 0?
- For what values of x, if any, does #f(x) = 1/((x+12)(x+6)) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((3x-2)sin(pi+(2pi)/x) # have vertical asymptotes?

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