Define horizontal asymptote to a curve y = f(x). Find the horizontal asymptote to the curve f(x) = frac5x2 + 8x - 33x2 + 2 and draw the curve. [2+3]

A line $y = L$ is called a horizontal asymptote to the curve $y = f(x)$ if the function approaches $L$ as $x$ tends to infinity in magnitude, i.e. $$\lim{x \to +\infty} f(x) = L \qquad \text{or} \qquad \lim{x \to -\infty} f(x) = L.$$ As $x \to \infty$, the perpendicular distance between the curve...