Value of $\lim\limits_{x\to-\infty}{(4x^2-x)^{1/2} +2x}$ The value of the $$\lim\limits_{x\to-\infty}{(4x^2-x)^{1/2} +2x}$$ is?
The answer given is $1/4$.
I rationalized and got $$\lim\limits_{x\to-\infty} \frac {-x}{|x|[(4- \frac {1}{x})^{1/2}-2]}$$ how to proceed further?

A more elementary solution :
$$\lim_{x\to -\infty} \big( \sqrt{4x^2-x} +2x \big) =\lim_{x\to -\infty} \frac{-x}{\sqrt{4x^2-x} -2x} =\lim_{x\to \infty} \frac{x}{\sqrt{4x^2+x}+2x} =\lim_{x\to\infty} \frac{1}{\sqrt{4+\frac{1}{x}}+2} = \frac{1}{\sqrt{4}+2}=\frac{1}{4}$$
where I used that
$$\lim_{x\to -\infty} f(x)=\lim_{x\to \infty} f(-x)$$
