How do you use L'hospital's rule to find the limit #lim_(x>oo)xsin(pi/x)# ?
To use L'Hôpital's Rule to find the limit lim(x→∞) x*sin(π/x), follow these steps:

Identify the indeterminate form of the limit as x approaches infinity, which is 0*∞.

Rewrite the limit as a fraction: lim(x→∞) sin(π/x) / (1/x).

Take the derivatives of the numerator and denominator separately.

Evaluate the derivatives and substitute them back into the original limit expression.

Repeat steps 3 and 4 as needed until the limit is no longer in an indeterminate form.

Evaluate the limit using the new expression.
Remember that L'Hôpital's Rule can only be applied when both the numerator and denominator approach either 0 or infinity as x approaches the limit.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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