How do you find the limit of #(2^x)/(3^x-2^x)# as #x->oo#?
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To find the limit of (2^x)/(3^x-2^x) as x approaches infinity, we can use the concept of limits.
First, we can rewrite the expression as (2^x)/(3^x(1-(2/3)^x)).
As x approaches infinity, (2/3)^x approaches 0 since the base (2/3) is less than 1.
Therefore, the denominator approaches 1 - 0 = 1.
The numerator, 2^x, grows exponentially as x approaches infinity.
Thus, the limit of (2^x)/(3^x-2^x) as x approaches infinity is infinity.
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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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