## appleduardo 3 years ago what is the limit for the next function?

1. appleduardo

$\frac{ x ^{4} -16 }{x ^{2} -2 }$

2. appleduardo

x--> 2

3. hartnn

can u factor x^4 -16 ?

4. hartnn

wait, is that x^2 -2 ?? if yes, there is no need to factor. just put x=2

5. appleduardo

mm maybe do this: x[x^(3) ] +16 ooh i was wrong, is x^(2) - 4

6. hartnn

x^4 -16 now 16 is 4^2 , isn't it ? so you can write numerator as $$\large (x^2)^2-4^2$$ use a^2-b^2 = .... formula, do u know ?

7. appleduardo

mm i dont remember! but once i have the numerator like that what can i do next?

8. hartnn

$$\large a^2-b^2=(a+b)(a-b) \\ \text {so what is} (x^2)^2-4^2$$

9. appleduardo

so i'll get (x+2)^(2) * ( x-2)^(2) ???

10. hartnn

?? no. $$\huge (x^2)^2-4^2=(x^2+4)(x^2-4)$$

11. appleduardo

ooh!! i understand now ! :D so then i can cancel x^(2) - 4 and the limit will be 8 right?

12. hartnn

YES.

13. appleduardo

Wow! you're awesome !! :D mm what about this one? $\frac{ \frac{ 1 }{ x } + \frac{ 1 }{ 2 }}{ x-2 }$ x-->2

14. hartnn

that limit does not exist!

15. appleduardo

mm why?

16. hartnn

u know the how to find lim x->2+ and lim x->2- or know what they are ?

17. appleduardo

mm i dont :/