# How do you find the limit of #(costheta-1)/sintheta# as #theta->0#?

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To find the limit of (cos(theta) - 1)/sin(theta) as theta approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (-sin(theta))/cos(theta). Evaluating this expression as theta approaches 0, we have (-sin(0))/cos(0) = 0/1 = 0. Therefore, the limit of (cos(theta) - 1)/sin(theta) as theta approaches 0 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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