# How do you estimate the instantaneous rate of change at the point for #x=5# for #f(x) = ln(x)#?

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To estimate the instantaneous rate of change at the point for (x = 5) for (f(x) = \ln(x)), you would use the derivative of the function (f(x)), which is (f'(x) = \frac{1}{x}). Then, evaluate (f'(x)) at (x = 5), which gives (f'(5) = \frac{1}{5}). Therefore, the instantaneous rate of change at the point (x = 5) for (f(x) = \ln(x)) is (\frac{1}{5}).

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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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