# How do you find the derivative of #0# using the limit definition?

The answer is 0.

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The derivative of zero is zero. This makes sense because it is a constant function.

Limit definition of derivative:

Zero is a function of x such that

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To find the derivative of a constant function (such as 0) using the limit definition of a derivative, you would use the following formula:

[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

For ( f(x) = 0 ), substituting into the formula gives:

[ f'(x) = \lim_{h \to 0} \frac{0 - 0}{h} = \lim_{h \to 0} \frac{0}{h} = \lim_{h \to 0} 0 = 0 ]

Therefore, the derivative of the constant function ( f(x) = 0 ) is 0.

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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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