What is the limit as $x$ $x$ approaches infinity of $\frac{x^{2} - 4}{2 x - 4 x^{2}}$ $(x^2-4)/(2x-4x^2)$ ?

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What is the limit as $x$ $x$ approaches infinity of $\frac{x^{2} - 4}{2 x - 4 x^{2}}$ $(x^2-4)/(2x-4x^2)$ ?

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Answer 1 · 2018-03-22T05:07:04

Stefan V.

Mar 22, 2018

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Answer 2 · 2018-03-22T13:52:36

$- \frac{1}{4}$ $-1/4$

Explanation:

$divide terms on numerator/denominator by the highest$ $"divide terms on numerator/denominator by the highest"$
$power of x, that is x^{2}$ $"power of x, that is "x^2$

$\Rightarrow \frac{\frac{x^{2}}{x^{2}} - \frac{4}{x^{2}}}{\frac{2 x}{x^{2}} - \frac{4 x^{2}}{x^{2}}} = \frac{1 - \frac{4}{x^{2}}}{\frac{2}{x} - 4}$ $rArr(x^2/x^2-4/x^2)/((2x)/x^2-(4x^2)/x^2)=(1-4/x^2)/(2/x-4)$

$rArrlim_(xtooo)(x^2-4)/(2x-4x^2)$

$=lim_(xtooo)(1-4/x^2)/(2/x-4)$

$=(1-0)/(0-4)=-1/4$

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What is the limit as $x$ $x$ approaches infinity of $\frac{x^{2} - 4}{2 x - 4 x^{2}}$ $(x^2-4)/(2x-4x^2)$ ?

2 Answers

Explanation:

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