Question

lim x--> infinity x-(x^2+2x-4)^1/2

Answer 1

If you plug in infinity you get \[\infty-\infty\]
so you have to rationalize, multiply it by x+(x^2+2x-4)^(1/2)/x+(x^2+2x-4)^1/2

Answer 2

Pretty sure it works out to -1.

Answer 3

\[\lim_{x \rightarrow \infty}\left( x-\sqrt{x^2 + 2x - 4} \right)\]\[\lim_{x \rightarrow \infty}\left( x-\sqrt{x^2 + 2x - 4} \right)\left(\frac{x+ \sqrt{x^2 + 2x - 4}}{x + \sqrt{x^2 + 2x - 4}}\right)\]\[\lim_{x \rightarrow \infty}\left( \frac{-2x + 4}{x + \sqrt{x^2 + 2x - 4}} \right)\left( \frac{\frac{1}{x}}{\frac{1}{x}} \right)\]\[\lim_{x \rightarrow \infty}\left( \frac{-2 + \frac{4}{x}}{1 + \sqrt{1 + \frac{2}{x}- \frac{4}{x^2}}} \right)\]\[\frac{-2 + 0}{1 + \sqrt{1 + 0 - 0}}=-1\]

Answer 4

thank you. i got up the point you multiplied and got confused from that point. but i got it now