How can find this limit? $\lim_{x\to-∞}(\sqrt{x^2+6x}-\sqrt{x^2-2x})$ $$\lim_{x\to-∞}(\sqrt{x^2+6x}-\sqrt{x^2-2x})$$
plugging in infinity gives infinity - infinity, what kind of manipulation can I do to solve this?
Exploit the identity:
$$\sqrt{x^2+6x}-\sqrt{x^2-2x} = \frac{8x}{\sqrt{x^2+6x}+\sqrt{x^2-2x}} = \frac{8x}{2|x|+O(1)}.$$
To conclude this The answer is actually -4 , because you can do this step