limit as x approaches negative infinity

• March 6th 2010, 06:33 PM
hangainlover
limit as x approaches negative infinity
as x approaches negative infinity, what value does this function approach ?
limit square root (X^2+X) + X

i manipulated it to take out absolute (x) from the square root

so, limit absolute value (x) square root (1+1/x) +x

now, i get infinity - infinity.
I do not know where to go from this point.

Thanks
• March 6th 2010, 11:08 PM
matheagle
I get -.5, but you need to be careful with the negative sign.
Moving an x through a square root is not x, but |x|=-x in this case.

let w=-x and then multiply top and bottom by the conjugate and see what you get.
• March 7th 2010, 03:51 AM
HallsofIvy
You mean, I take it, $\lim_{x\to -\infty} \sqrt{x^2+ x}+ x$.

Yes, matheagle is right. Multiplying "numerator and denominator" by $\sqrt{x^2+ x}- x$ give a limit of $-\frac{1}{2}= -0.5$.