Question

Find the limit: lim as x approaches infinity of (x-sqrt(x^2+ x))

Answer 1

(x - √(x²+x)) * (x + √(x²+x)) / (x+√(x²+x))

(x - (x²+x)) / (x+√(x²+x))

-x² / (x + √(x²+x))

Answer 2

multiply top and bottom by 1/x^2, i'll leave the rest to you

Answer 3

Thank you so much! That helps a lot. I think I can figure it out from there

Answer 4

Careful! you should get \(\large \displaystyle\lim_{x\to\infty} \frac{-x}{x+\sqrt{x^2+x}}\) after multiplying the original limit by the conjugate; this limit goes to a finite value. On the other hand, \(\large \displaystyle\lim_{x\to\infty} \frac{-x^2}{x+\sqrt{x^2+x}}=-\infty\).