# What is #lim_(xrarr0+) ( x )^(2x)#?

Thus, we can use the Rule of Hospitality:

We draw the conclusion that

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The limit of (x)^(2x) as x approaches 0 from the positive side 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 use the epsilon delta definition of limit to prove that #lim_(x->5)(x-1)= 4# ?
- How do you find the Limit of #ln(x+1)/x # as x approaches infinity?
- How do you find the limit of #|x+2| / (x+2)# as x approaches #-2#?
- How do you find the limit of #cosx/cotx# as #x->pi/2#?
- How do you find the limit of #e^(x-x^2)# as #x->oo#?

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