Question

lim x-> inf. (sqrt(x^2+10x) - sqrt(x^2 + 5x))

Answer 1

hint\[\sqrt{x^2+10x} - \sqrt{x^2 + 5x}=\sqrt{x^2+10x} - \sqrt{x^2 + 5x}\times \frac{\sqrt{x^2+10x} + \sqrt{x^2 + 5x}}{\sqrt{x^2+10x} + \sqrt{x^2 + 5x}}\]\[\frac{5x}{\sqrt{x^2+10x} + \sqrt{x^2 + 5x}}\]divide num and denum by x\[\frac{5}{\sqrt{1+\frac{10}{x}} + \sqrt{1 + \frac{5}{x}}}\]