# How do you find the average rate of change of #f(x) = tan(x)# from #x=0# to #x=pi/4#?

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To find the average rate of change of the function (f(x) = \tan(x)) from (x = 0) to (x = \frac{\pi}{4}), you can use the formula:

[ \text{Average rate of change} = \frac{f(\text{end}) - f(\text{start})}{\text{end} - \text{start}} ]

Substitute the given values into the formula:

[ \text{Average rate of change} = \frac{\tan\left(\frac{\pi}{4}\right) - \tan(0)}{\frac{\pi}{4} - 0} ]

[ \text{Average rate of change} = \frac{1 - 0}{\frac{\pi}{4}} ]

[ \text{Average rate of change} = \frac{4}{\pi} ]

So, the average rate of change of (f(x) = \tan(x)) from (x = 0) to (x = \frac{\pi}{4}) is ( \frac{4}{\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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