Question

find the limit

Answer 1

\[\lim_{x \rightarrow \infty} \sqrt{x^2-2x}-x\]

Answer 2

multiply top and bottom by the conjugate of the top

Answer 3

\[\lim_{x \rightarrow \infty}\frac{(x^2-2x)-x^2}{\sqrt{x^2-2x}+x}\]

Answer 4

x^2-x^2=0
now divide both top and bottom by sqrt{x^2}
remember sqrt{x^2}=|x|
|x|=x if x>0
|x|=-x if x<0
since x-> positive infinity then |x|=x