anonymous one year ago lim f(x) as x-> 2- and lim f(x) as x-> 2+ help explain graphs of limits to me?

1. anonymous

2. anonymous

So how does the graph explain what the limit is?

3. ganeshie8

For $$\large \lim\limits_{x\to 2^{-}} f(x)$$, imagine yourself walking on the graph towards x=2 from the left of "x=2" |dw:1433302549455:dw|

4. anonymous

Okay, that is helpful. Can you explain what the dot on the graph represents?

5. ganeshie8

you're staying on y=f(x)=3, so the left limit is 3 : $\large \lim \limits_{x\to2^{-}}f(x) ~~=~~3$

6. ganeshie8

similarly see if you can find the right limit : $\large \lim \limits_{x\to2^{+}}f(x) ~~=~~?$

7. anonymous

-3 ?

8. ganeshie8

Excellent! the "dot" represents the value of function exactly at x = 2

9. ganeshie8

|dw:1433302827174:dw|

10. anonymous

Oh okay. so for this one would it be 4?

11. ganeshie8

Yes! the right hand side limit is 4

12. anonymous

Okay, now i understand what the difference in the two limits is. Thank you!

13. ganeshie8

Yw!