# Thread: Limit question

1. ## Limit question

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..

2. Originally Posted by Monster32432421
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..

Try to rationalise the numerator .

3. Originally Posted by Monster32432421
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

4. also a little care , you may make mistakes very easily .

5. Originally Posted by tonio
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
thanks

6. $\displaystyle {\sqrt{4x^2+7x-2}\over x} = \sqrt{4x^2+7x-2\over x^2} = \sqrt{4 + \frac7x -\frac2{x^2}}$