# How do you prove that #lim_(x->5)x^2!=24# using limit definition?

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How do you prove that #lim_(x->5)x^2!=24# using limit definition?

How do you prove that

##### 1 Answer

Pose

Using the reverse triangular inequality we can state that:

Consider now any

We have that for

and based on the triangular inequality:

If we choose

so that based on

So if we choose any

which contradicts the limit definition.