limit as x approaches negative infinity 3x/(4x^2+10)^(1/2)

why is this -3/2 instead of 3/2 if you end up with 3/(2+10^(1/2)/x)

Question

limit as x approaches negative infinity 3x/(4x^2+10)^(1/2)


why is this -3/2 instead of 3/2 if you end up with 3/(2+10^(1/2)/x)

anonymous · Answer

why would you  do that?

anonymous · Answer

I thought you just divided by biggest x^n

zarkon · Answer

$$\sqrt{4x^2+10}=\sqrt{x^2}\sqrt{4+\frac{10}{x^2}}=|x|\sqrt{4+\frac{10}{x^2}}$$

zarkon · Answer

then for $x<0$ we have $$\frac{x}{|x|}=-1$$

turingtest · Answer

dang, this is trickier than I anticipated
I like Zarkon's way but I'm, trying to find another

anonymous · Answer

gahh i hate theory, is there any other way to explain it having to do that would be a huge pain in the retriceon the test I'm going to have to remember that specifically. I didn't even know you could relate (x^2)^(1/2) to abs(x). How is that I get a 100% on the first test to not understanding what is going on at all...

turingtest · Answer

actually the definition of $$|x|=\sqrt{x^2}$$that is a good thing to know in general

turingtest · Answer

latex question:
how do you write the defined as symbol?

zarkon · Answer

this?

$$\equiv$$

zarkon · Answer

I usuallt just use 

:=

so $$|x|:=\sqrt{x^2}$$

anonymous · Answer

I wish they would have taught us this earlier.... lol

zarkon · Answer

usually it is written as 

$$|x|=\left\{\begin{matrix}x & \text{if}& x\ge0 \-x & \text{if}&x<0\end{matrix}\right.$$

turingtest · Answer

I mine wrong? I know they use it for some proofs

turingtest · Answer

is*

zarkon · Answer

$$|x|=\sqrt{x^2}$$ is a valid definition