appleduardo
what is the limit for the next function?



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

appleduardo
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x> 2

hartnn
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can u factor x^4 16 ?

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

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

hartnn
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x^4 16
now 16 is 4^2 , isn't it ?
so you can write numerator as
\(\large (x^2)^24^2\)
use a^2b^2 = .... formula, do u know ?

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

hartnn
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\(\large a^2b^2=(a+b)(ab) \\ \text {so what is} (x^2)^24^2 \)

appleduardo
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so i'll get (x+2)^(2) * ( x2)^(2) ???

hartnn
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?? no.
\(\huge (x^2)^24^2=(x^2+4)(x^24)\)

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

hartnn
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YES.

appleduardo
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Wow! you're awesome !! :D mm what about this one? \[\frac{ \frac{ 1 }{ x } + \frac{ 1 }{ 2 }}{ x2 }\] x>2

hartnn
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that limit does not exist!

appleduardo
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mm why?

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

appleduardo
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mm i dont :/