How do you find the limit of #e^(x-x^2)# as #x->oo#?

Answer 1

# lim_(x rarr oo) e^(x-x^2) = 0 #

This is not a vigorous proof but should be convincing enough for most college maths:

We have # e^(x-x^2) = e^(x(1-x)) #
As #x rarr oo # then # 1-x ~~ -x => x(1-x) ~~ (x)(-x) = -x^2 # So, As #x rarr oo # then # e^(x(1-x)) ~~e^(-x^2) rarr 0 #
Hence, # lim_(x rarr oo) e^(x-x^2) = 0 #
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Answer 2

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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Answer from HIX Tutor

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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