Question

About limit function, solve this


`\lim \limits_(x \to2) \frac{ {x}^(2) - 4 }{x - 2} =`
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Answer 1

`\lim \limits_(x \to2) \frac{ {x}^(2) - 4 }{x - 2} \\ = \lim \limits_(x \to2) \frac{ {(x)}^(2) - {(2)}^(2) }{x - 2} \\ = \lim \limits_(x \to2) ( ( x- 2)(x + 2) )/(x - 2) \\ = \lim \limits_(x \to2) ( x+ 2) \\ = 2 + 2 \\ = 4`

Answer:

4

Hope you could understand.

If you have any query, feel free to ask.

Answer 2

The limit of the function as x approaches 2 is 4.

Explanation:

This function just simplifies to
`x+2`:

`(x^2-4)/(x-2)\\\\((x+2)(x-2))/(x-2)\\\\x+2`

That leaves us with this:

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`\lim_(x\to2)x+2`

This is a simple linear function that can be evaluated at
`x=2`:

`f(x)=x+2\\f(2)=2+2\\f(2)=4`

The values also exist on either side of this point.

`f(1.999)=3.999\\f(2.001)=4.001`