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Vn Method

Evaluate the ...

Question

Evaluate the limit to infinity
$lim x \to \infty \frac{{a x}^{2} + b x + c}{{d x}^{2} + e x + f} = \frac{a}{d}$

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Solution

$lim x \to \infty \frac{a x^{2} + b x + c}{d x^{2} + e x + f}$

$= lim x \to \infty \frac{x^{2} (a + \frac{b}{x} + \frac{c}{x^{2}})}{x^{2} (d + \frac{e}{x} + \frac{f}{x^{2}})} = \frac{a}{d}$

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