# How do you use L'hospital's rule to find the limit #lim_(x->oo)x^(1/x)# ?

To find the limit lim_(x->∞)x^(1/x) using L'Hôpital's Rule, we can rewrite the expression as e^(ln(x) / x). Then, apply L'Hôpital's Rule by taking the derivative of the numerator and the derivative of the denominator separately.

lim_(x->∞) e^(ln(x) / x)

= lim_(x->∞) e^(ln(x) / x)

= e^lim_(x->∞) (ln(x) / x)

Now, apply L'Hôpital's Rule to the limit inside the exponential function:

lim_(x->∞) (ln(x) / x) = lim_(x->∞) (1/x) / 1

= lim_(x->∞) 1 / x

= 0

Therefore, the original limit is:

e^0 = 1

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The basic idea in using the rule of De l'Hospital to find indeterminate limits of powers

If the power was indeterminate (

In this example

Thus

See this video on indeterminate powers for more:

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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.

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