# What are the three conditions for continuity at a point?

A function

#f(a)# is defined;#lim_(xrarra) f(x)# is defined; and#lim_(xrarra) f(x) =b#

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The three conditions for continuity at a point are:

- The function must be defined at that point.
- The limit of the function as x approaches that point must exist.
- The value of the function at that point must be equal to the limit 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^2+1)^3 (x+3)^5# as x approaches -1?
- How do you find the Limit of #[(sin x) * (sin^2 x)] / [1 -( cos x)]# as x approaches 0?
- What is the limit of #(-2x+11)# as x approaches infinity?
- How do you find the limit of #(sin(x)/3x) # as x approaches 0 using l'hospital's rule?
- How do you evaluate the limit #(sqrt(x+6)-x)/(x-3)# as x approaches #3#?

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