Question

limit as x->-∞ from (4x^3+2)/(x^3+√(4x^6+1)
I know is -4 I'd like to see how you guys do it .

Answer 1

factor out an \(x^3\) from the top and bottom.

Answer 2

notice \[\sqrt{x^6}=|x^3|\]

Answer 3

\[\lim_{x\to-\infty}{4x^3+2\over x^3+\sqrt{4x^6+1}}\]yup easiest way^

Answer 4

How do you isolate \(x^3\) from \(\sqrt{4x^6+1}\). All I see is\[\sqrt{x^6(4+x^{-6})}\]

Answer 5

I would've suggested multiplying by the reciprocal.

Answer 6

@badreferences

use my second post

Answer 7

I still don't see it.\[\sqrt{4x^6+1}=\sqrt{x^6\left(4+x^{-6}\right)}=\left|x^3\right|\sqrt{4+x^{-6}}\]If you don't mind me asking.

Answer 8

right...and if \(x<0\) then \(|x^3|=-x^3\)

Answer 9

4/(1-2) ..

Answer 10

oh, okay, I see it. then afterwards multiply by \[1+\sqrt{4+x^{-6}}\] reciprocal

Answer 11

you don't need to

Answer 12

oh, find the limit. not simplify. sorry, wasn't reading.

Answer 13

just let \(x\to-\infty\)

Answer 14

my problem ... |x^3| = -x^3

Answer 15

\[|x|=\left\{\begin{matrix}x & if & x\ge 0 \\ -x & if & x<0\end{matrix}\right.\]

Answer 16

replace \(x\) by \(x^3\)

Answer 17

right ...

Answer 18

THX

Answer 19

no problem