# How do you use the limit definition to compute the derivative, f'(x), for #5x^2-3x+7#?

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To compute the derivative ( f'(x) ) of ( 5x^2 - 3x + 7 ) using the limit definition, follow these steps:

- Start with the function ( f(x) = 5x^2 - 3x + 7 ).
- Use the definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ).
- Substitute the given function into the definition: ( f'(x) = \lim_{h \to 0} \frac{(5(x+h)^2 - 3(x+h) + 7) - (5x^2 - 3x + 7)}{h} ).
- Expand and simplify the expression inside the limit.
- Compute the limit as ( h ) approaches 0.

After performing these steps, you will have found the derivative ( f'(x) ) of the function ( 5x^2 - 3x + 7 ) using the limit definition.

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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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