# How do you find the limit #cosx/(pi/2-x)# as #x->pi/2#?

Because the expression evaluated at the limit results in an indeterminate form (specifically

Using L'Hôpital's rule , we compute the derivative of the numerator and the denominator:

Assemble the new expression and evaluate at the limit:

According to the rule, the original limit goes to the same value:

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If you have not yet learned l'Hospital's Rule, then see below.

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To find the limit of cosx/(pi/2-x) as x approaches pi/2, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, we get -sinx/(-1), which simplifies to sinx. Evaluating this expression at x = pi/2, we find that the limit is equal to 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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