# What is the limit of #x^(1/x)# as #x->oo#?

therefore we can apply L'Hospital's Rule and

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

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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.

- How do you evaluate the limit #(1+1/sqrtx)^x# as x approaches #oo#?
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- What is the limit of #(1+e^x)^(1/x)# as x approaches infinity?
- Evaluate the limit? # lim_(x rarr 0) (1-cos2x+tan^2x)/(xsin2x) #
- How do you evaluate the limit #(1/(1+h)-1)/h# as h approaches #0#?

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