What is the limit definition of the derivative of the function #y=f(x)# ?
There are several ways of writing it. They all capture the same idea.
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The limit definition of the derivative of a function ( y = f(x) ) is given by:
[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]
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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.
- What is the equation of the line normal to #f(x)= sqrt(3x^3-2x) # at #x=2#?
- How do you find the equation of a line tangent to the function #y=x^3+6# at (1,7)?
- How do you find the tangent line of #f(x) = 3x/sinx^2 # at x=5?
- How do you find the derivative of #2/sqrtx# using the limit definition?
- How do you find the average rate of change of #y=4x-3x^2# over [2,3]?

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