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

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To find the limit of (x - π/2)tan(x) as x approaches π/2, we can use the concept of L'Hôpital's Rule.

First, we differentiate both the numerator and denominator with respect to x. The derivative of (x - π/2) is 1, and the derivative of tan(x) is sec^2(x).

Next, we substitute π/2 into the derivatives to get 1/(sec^2(π/2)). Since sec^2(π/2) is equal to 1, the limit simplifies to 1/1, which is equal to 1.

Therefore, the limit of (x - π/2)tan(x) as x approaches π/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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- How do you find the limit of #1 / (x - 2)^2# as x approaches 2?

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