Limit when x approaches C

[Sam007]

Hi everyone,

I received this as an extension question and don't really know how to solve it.

Your help will be greatly appreciated.

 

[Otis]

Hello.

f(x) = y, so the limit is about y.

When a limit says x→c, it means the limit exists only if y approaches the same value, as x approaches c from both the left and the right. (We call this a 'double-sided' limit statement.)

Look at the graph as x→-2

Does y approach the same value, as x approaches -2 from both the left and the right? No, it doesn't. That limit does not exist.

What do you think about the other two?

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[Sam007]

I think the answer is 3 as right hand and left hand limits both approach the same value (−1). While on the other two points, the left and right hand limits reach different values.

Is that a correct understanding?

 

[Otis]

Yup!

If you were asked to find the limit as x→ -1, what would you write?

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