# How do you determine the limit of #(pi/2)-(x)/(cos(x))# as x approaches pi/2?

The limit does not exist, but

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To determine the limit of (pi/2) - (x)/(cos(x)) as x approaches pi/2, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately and then evaluate the limit of the resulting expression.

Differentiating the numerator, we get -1, and differentiating the denominator, we get -sin(x).

Now, substituting x = pi/2 into the differentiated expressions, we have -1 for the numerator and -sin(pi/2) = -1 for the denominator.

Therefore, the limit of (pi/2) - (x)/(cos(x)) as x approaches pi/2 is -1/-1, which simplifies 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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- How you solve this? #lim_(n->oo)prod_(k=1)^n((k+1)^2)/(k(k+2))#

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