Using the limit definition, how do you find the derivative of #f(x) = 3x^2 + 8x + 4 #?
Applying the limit definition, we obtain
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To find the derivative of ( f(x) = 3x^2 + 8x + 4 ) using the limit definition, follow these steps:
- Begin with the definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ).
- Substitute the given function ( f(x) = 3x^2 + 8x + 4 ) into the formula.
- Expand the function ( f(x + h) ) and ( f(x) ).
- Simplify the expression by combining like terms.
- Take the limit as ( h ) approaches 0.
- Calculate the derivative.
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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.
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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- What is the equation of the normal line of #f(x)=1/(2x^2-1)# at #x = 1#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(x) = 7 # at (-4,7)?

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