# How do you find the limit of #(x^(2)/(sinx-x))# as x approaches 0?

I think that the limit does not exists but you can find the lateral ones!

graph{x^2/(sin(x)-x) [-10, 10, -5, 5]}

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To find the limit of (x^2/(sinx-x)) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (2x)/(cosx-1). Evaluating this expression as x approaches 0, we find that the limit 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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