# If # f(x) = { (x^2, x !=2), (2, x=2) :} # then evaluate # lim_(x rarr 2) f(x)#?

# lim_(x rarr 2) f(x) = 4#

In order to evaluate a limit we are not interested in the value of the function at the limit, just the behaviour of the function around the limit:

We have:

The Left Handed limit:

And The Right Handed limit:

And as both limits are identical we have:

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Please see the discussion below.

Finally, functions like the one in this question (kind of strange, with weird points) are very important to learning the difference between:

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The limit of f(x) as x approaches 2 is equal to 4.

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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.

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- How do you find the limit of #(3x +9) /sqrt (2x^2 +1)# as x approaches infinity?
- How do you find the limit of #((e^x)-x)^(2/x)# as x approaches infinity?

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