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

#x->(pi)/2# so#cosx!=0#

So we need to calculate this limit

because

Some graphical help

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For an algebraic solution, please see below.

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To determine the limit of (x - π/2)tan(x) as x approaches π/2, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate both the numerator and denominator separately with respect to x.

Differentiating the numerator (x - π/2) gives us 1, and differentiating the denominator tan(x) gives us sec^2(x).

Now, we substitute x = π/2 into the differentiated numerator and denominator. We get 1/sec^2(π/2), which simplifies to 1/cos^2(π/2).

Since cos(π/2) equals 0, the denominator becomes 0, and the limit is undefined.

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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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