find the limit: lim((square root of 4x^2+5x)-2x)) as x approaches to negative infinity. Show the process. find the limit: lim((square root of 4x^2+5x)-2x)) as x approaches to negative infinity. Show the process. @Mathematics

Question

anonymous · Answer

i think it is 
$$\frac{5}{4}$$

anonymous · Answer

oh scratch that.  x is going to minus infinity. i changed my mind.

anonymous · Answer

if x is going to minus infinity it is not "indeterminate" form. it is just 
$$\infty+\infty=\infty$$

anonymous · Answer

trick question!

agreene · Answer

Actually, this isnt an indeterminate form, nor is it complex infty. You just need to do some re-arranging, it will come out to infinity.

agreene · Answer

$$\large\sqrt{\lim_{x \rightarrow -\infty} 4x^2+5x}-2\lim_{x\rightarrow -\infty}x$$

Is the same thing as the original question.

agreene · Answer

So, we can see we get 
infty+infty = infty
which is defined.

anonymous · Answer

so what is the process to solution? can you write more?

agreene · Answer

That basically is the process, 
Once you move the limits, it's clear you are going to have:
infty - -infty
infty+infty = infty.

anonymous · Answer

oh ok. thanks.