`lim_{x -> -\infty} (sqrt{4x^2 - 3} - x)`
`= lim_{x -> -\infty} (4x^2 - 3 - x^2)/(\sqrt{4x^2 - 3} + x)`
`= lim_{x -> -\infty} (3x^2 - 3)/(\sqrt{4x^2 - 3} + x)`
`= lim_{x -> -\infty}` $\dfrac{3 - \dfrac{3}{x^2}}{\sqrt{\dfrac{4}{x^2} - \dfrac{3}{x^4}} + \dfrac{1}{x}}$
`= (3 - 0)/(0)`
`= +infty`
`lim_{x -> +\infty} (x - sqrt{x^2 + 5x))`
`= lim_{x -> +\infty} (x^2 - x^2 - 5x)/(x + \sqrt{x^2 + 5x})`
`= lim_{x -> +\infty} (-5x)/(x + \sqrt{x^2 + 5x})`
`= lim_{x -> +\infty}` $\dfrac{-5}{1 + \sqrt{1 + \dfrac{5}{x}}}$
`= (-5)/(1 + 1)`
`= -5/2`
`lim_{x -> +\infty} (x - ` $\sqrt[3]{x^3 + 5x})$
`= lim_{x -> +\infty}` $\dfrac{x^3 - x^3 - 5x}{x^2 + x\sqrt[3]{x^3 + 5x} + (\sqrt[3]{x^3 + 5x})^2}$
`= lim_{x -> +\infty}` $\dfrac{-5x}{x^2 + x\sqrt[3]{x^3 + 5x} + (\sqrt[3]{x^3 + 5x})^2}$
`= lim_{x -> +\infty}` $\dfrac{\dfrac{-5}{x}}{1 + \sqrt[3]{1 + \dfrac{5}{x^2}} + (\sqrt[3]{1 + \dfrac{5}{x^2}})^{2}}$
`= 0`
