# How do you find f'(2) using the limit definition given #f(x)= 9-x^2#?

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Using the limit definition, you get:

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To find ( f'(2) ) using the limit definition given ( f(x) = 9 - x^2 ), follow these steps:

- Start with the function ( f(x) = 9 - x^2 ).
- Find ( f'(x) ), the derivative of ( f(x) ), using the limit definition of the derivative.
- Evaluate ( f'(x) ) at ( x = 2 ).

Here's how to proceed:

- ( f(x) = 9 - x^2 )
- ( f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} )
- ( f'(x) = \lim_{h \to 0} \frac{(9 - (x + h)^2) - (9 - x^2)}{h} ) 4

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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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