# What is the limit of #(e^x + x)^(1/x)# as x approaches infinity?

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We can move the limit inside of the exponential function:

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The limit of (e^x + x)^(1/x) as x approaches infinity is e.

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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.

- What is #lim_(xrarroo) (3x^3+2x+500x-1)/(x^4-8000x^3-30x) #?
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- How do you find the Limit of #(x/lnx)# as x approaches infinity?
- How do you solve for #x in RR# the equation #x! = e^x# ?
- How do you find the limit of #x^2-2x# as x approaches 2?

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