How do you find the limit of #e^(x-x^2)# as #x->oo#?
This is not a vigorous proof but should be convincing enough for most college maths:
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To find the limit of e^(x-x^2) as x approaches infinity, we can analyze the behavior of the function as x becomes larger and larger.
As x approaches infinity, the term x^2 grows much faster than x. Therefore, the x^2 term dominates the expression x-x^2, causing it to approach negative infinity.
Since e^(-∞) approaches 0, the limit of e^(x-x^2) as x approaches infinity is 0.
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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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