# How do you find the limit of #(arctan(5x))/(sin(7x))# as x approaches 0?

This is an indeterminate type so we use the l'Hopitals'Rule. That is, find the limit of the derivative of the top divided by the derivative of the bottom.

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To find the limit of (arctan(5x))/(sin(7x)) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (5)/(7cos(7x)). Evaluating this expression as x approaches 0, we find that the limit is 5/7.

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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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