# What is the limit of #x^2sin(1/x)# as x approaches infinity?

If we rewrite the limit as...

Now we apply L'Hospital's Rule

Simplifying:

Now using direct substitution we'll find the limit to be...

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The limit of x^2sin(1/x) as x approaches infinity is 0.

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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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