Question

$\lim_{x \rightarrow \infty}\frac{ax^{2} + bx + c}{dx^{2} + ex + f}$=

• A. $\frac{b}{e}$
• B. $\frac{c}{f}$
• C. $\frac{a}{d}$
• D. $\frac{d}{a}$

Answer 1

Answer: (C)

$\frac{a}{d}$

Answer 2

Here the expression assumes the form $\frac{\infty}{\infty}$. We note that the highest power of x in both the numerator and denominator is 2. So we divide each terms in both the numerator and denominator by $x^{2}$.

$\lim_{x \rightarrow \infty}\frac{ax^{2} + bx + c}{dx^{2} + ex + f} = \lim_{x \rightarrow \infty}\frac{a + \frac{b}{x} + \frac{c}{x^{2}}}{d + \frac{e}{x} + \frac{f}{x^{2}}} = \frac{a + 0 + 0}{d + 0 + 0} = \frac{a}{d}$.