Question

lim x->inf
(5x-sqrt(25x^2+9x))

Answer 1

\[\lim_{x \rightarrow \infty}5x-\sqrt{25x^2+9x}\]\[=\lim_{x \rightarrow \infty}5x-\sqrt{25x^2+9x}\times \frac{5x+\sqrt{25x^2+9x}}{5x+\sqrt{25x^2+9x}}\]\[=\lim_{x \rightarrow \infty}\frac{25x^2-(25x^2+9x)}{5x+\sqrt{25x^2+9x}}\]\[=\lim_{x \rightarrow \infty}\frac{-9x}{5x+\sqrt{25x^2+9x}}\]Can you continue from here?

Answer 2

The two 25x^2 just cancel out right? how is there a negative left over