What is the limit of #(x^2-4)/(2x-4x^2)# as x goes to infinity?
It is
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The limit of (x^2-4)/(2x-4x^2) as x goes to infinity is 0.
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To find the limit of (x^2 - 4) / (2x - 4x^2) as x approaches infinity, we can look at the highest power terms in the numerator and denominator. In this case, the highest power terms are -4x^2 in the denominator and x^2 in the numerator. As x approaches infinity, the term -4x^2 in the denominator dominates the expression. Thus, the limit approaches -4/(-4), which simplifies to 1. Therefore, the limit of the given expression as x goes to infinity is 1.
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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.
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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- How do you find the limit of #(1-4x)^(6/x)# as x approaches 0?
- What is the limit as x approaches 0 of #tan(x)/sin(x)#?
- How do you find the limit of #( ln(4x) - ln(x) ) / ( ln(x) )# as x approaches 1?

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