LIMITS

Question

LIMITS

amtran_bus · Answer

I need help understand the open circles!

amtran_bus · Answer

Especially parts B and E.

ganeshie8 · Answer

+  means right side
- means left side

amtran_bus · Answer

Right. I understand the left and right hand limits.

amtran_bus · Answer

Why is part e e when part F is no ans?

ganeshie8 · Answer

Notice that at x=4, the function is NOT DEFINED.

ganeshie8 · Answer

however at x = 4,  both left and right limits are approaching the same value of y = 4
So the limit exists at x = 4 even though the function is NOT defined.

ganeshie8 · Answer

does that answer your question ? :)

amtran_bus · Answer

So even if there is an open circle, you can still have a limit, but it may not be defined?

ganeshie8 · Answer

Exactly ! limit is about what happens when u approach a specific point - 
Limit is NOT about what happens exactly at a specific point.

amtran_bus · Answer

Thanks!!!!

ganeshie8 · Answer

np :) it was a good question !

amtran_bus · Answer

Hey, can you explain this to me?

because the right to left most curve come no where close to -3...

ganeshie8 · Answer

when x = -3, the function seem to approach 4 from both sides, eh ?

amtran_bus · Answer

You mean from both separate curves or a single one?

amtran_bus · Answer

Because if that is the case, how is this correct?

ganeshie8 · Answer

attachment

ganeshie8 · Answer

how are they related ?

amtran_bus · Answer

I thought the curve in the circle is the only one I could use for 5. |dw:1402342251125:dw|