# How do you find the limit of #tan(pi*x)/x# as x approaches 0?

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To find the limit of tan(pi*x)/x as x approaches 0, we can use the concept of limits in calculus. By applying L'Hôpital's rule, we can differentiate the numerator and denominator separately and then evaluate the limit.

Differentiating the numerator, we get the derivative of tan(pi*x) which is sec^2(pi*x) * pi.

Differentiating the denominator, we get the derivative of x which is 1.

Now, we can rewrite the limit as the limit of (sec^2(pi*x) * pi) / 1 as x approaches 0.

Since sec^2(pi*x) approaches 1 as x approaches 0, the limit simplifies to pi.

Therefore, the limit of tan(pi*x)/x as x approaches 0 is equal to pi.

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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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