Question

what is the limit for the next function?

Answer 1

\[\frac{ x ^{4} -16 }{x ^{2} -2 }\]

Answer 2

x--> 2

Answer 3

can u factor x^4 -16 ?

Answer 4

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

Answer 5

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

Answer 6

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 ?

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

YES.

Answer 13

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

Answer 14

that limit does not exist!

Answer 15

mm why?

Answer 16

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

Answer 17

mm i dont :/