# How do you use the limit definition to find the derivative of #f(x)=(2-x)/(3x+1)#?

Calculate:

Passing to the limit:

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To use the limit definition to find the derivative of the function (f(x) = \frac{2 - x}{3x + 1}), you first find the difference quotient (\frac{f(x + h) - f(x)}{h}), then take the limit as (h) approaches (0). This gives the derivative of the function (f(x)).

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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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- What is the equation of the line tangent to # f(x)=1/ln(x^2+x)*(x^2+x) # at # x=-1 #?
- How do you determine the rate of change of a function?
- How do you use the limit definition of the derivative to find the derivative of #f(x)=3x^2#?

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