# 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.

- What is the limit of #(3x^2 - x + 4) / (2x^2 + 5x - 8)# as x approaches infinity?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(x^2-100) / (x+10) #?
- Where is the function #f(x) = x^4-1/x^2# discontinuous?
- How do you find the limit of #3x+2# as #x->-3#?
- How do you evaluate the limit #(1-cosx)/x# as x approaches #0#?

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