# 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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