How do you find the limit #lim_(x>0)tan(x)/x# ?
by the Product Rule,
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To find the limit (\lim_{x \to 0} \frac{\tan(x)}{x}), you can use L'Hôpital's Rule, which states that if you have an indeterminate form (\frac{0}{0}) or (\frac{\infty}{\infty}) when evaluating a limit, you can differentiate the numerator and denominator separately until you obtain a determinate form. In this case:

Differentiate the numerator and denominator separately: [ \lim_{x \to 0} \frac{\tan(x)}{x} = \lim_{x \to 0} \frac{\frac{d}{dx} \tan(x)}{\frac{d}{dx} x} ] [ = \lim_{x \to 0} \frac{\sec^2(x)}{1} ]

Evaluate the limit: [ = \frac{\sec^2(0)}{1} = \frac{1}{1} = 1 ]
So, (\lim_{x \to 0} \frac{\tan(x)}{x} = 1).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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