# How do you find the limit of #cosx/(1-sinx)# as x approaches pi/2+?

Use L'Hôpital's rule to discover that it approaches infinity as x approaches

To implement the rule, take the derivative of the numerator:

take the derivative of the denominator.

Assemble this into a fraction:

Please observe that the above is the tangent function:

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Multiply by

So

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To find the limit of cosx/(1-sinx) as x approaches pi/2+, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, we get -sinx and -cosx, respectively. Evaluating the limit of these derivatives as x approaches pi/2+, we find that both approach -1. Therefore, the limit of cosx/(1-sinx) as x approaches pi/2+ is -1.

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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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