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

Answer 1

The answer is 0.

#f'(x) = lim_(h->0) ((0-0)/h) = lim_(h->0) 0 = 0 #
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Answer 2

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

Limit definition of derivative:

#f'(x) = lim_(hrarr0) (f(x+h) - f(x))/h#

Zero is a function of x such that

#f(x) = 0# #AA x#
So #f(x+h) = f(x) = 0#
#f'(x) = lim_(hrarr0)(0-0)/h = lim_(hrarr0) 0 = 0#
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Answer 3

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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Answer from HIX Tutor

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.

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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