# How do you find the limit of # (x^2-4)/(2x-4x^2)# as x approaches infinity?

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To find the limit of (x^2-4)/(2x-4x^2) as x approaches infinity, we can divide both the numerator and denominator by x^2. This gives us (1-4/x^2)/(2/x-4). As x approaches infinity, 4/x^2 approaches 0 and 2/x approaches 0. Therefore, the limit simplifies to (1-0)/(0-4), which is equal to -1/4. Hence, the limit of (x^2-4)/(2x-4x^2) as x approaches infinity is -1/4.

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To find the limit of ( \frac{x^2 - 4}{2x - 4x^2} ) as ( x ) approaches infinity, we first need to analyze the degrees of the numerator and denominator polynomials. Since the highest power of ( x ) in the numerator and denominator is ( x^2 ), we divide both the numerator and denominator by ( x^2 ) to simplify the expression.

[ \lim_{x \to \infty} \frac{x^2 - 4}{2x - 4x^2} = \lim_{x \to \infty} \frac{\frac{x^2}{x^2} - \frac{4}{x^2}}{\frac{2x}{x^2} - \frac{4x^2}{x^2}} ]

[ = \lim_{x \to \infty} \frac{1 - \frac{4}{x^2}}{\frac{2}{x} - 4} ]

As ( x ) approaches infinity, ( \frac{4}{x^2} ) and ( \frac{2}{x} ) both approach ( 0 ), leaving us with:

[ = \frac{1 - 0}{0 - 4} = \frac{1}{-4} ]

[ = -\frac{1}{4} ]

Therefore, the limit of ( \frac{x^2 - 4}{2x - 4x^2} ) as ( x ) approaches infinity is ( -\frac{1}{4} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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