Determine Lim x->Infinity Sqrt[4 x^2 + 7 x - 2] - (2 x + 1)
I know the answer, but i dont know the steps to get to it..
Write $\displaystyle \left[\sqrt{4x^2+7x-2}-(2x+1)\right]\,\frac{\sqrt{4x^2+7x-2}+(2x+1)}{\sqrt{4x^2+7x-2}+(2x+1)}$ $\displaystyle =\frac{3x-3}{\sqrt{4x^2+7x-2}+(2x+1)}$ , and now multiply the right hand by $\displaystyle \frac{1/x}{1/x}$ and do
a little algebra + some arithmetic of limits.
The limit is $\displaystyle \frac{3}{4}=0.75$
Tonio