# How do you find the average rate of change of #h(x) = x^3 − 1/5e^x# from [0,1]?

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To find the average rate of change of a function ( h(x) ) over an interval ([a, b]), you use the formula:

[ \text{Average rate of change} = \frac{h(b) - h(a)}{b - a} ]

Applying this formula to the function ( h(x) = x^3 - \frac{1}{5}e^x ) over the interval ([0,1]), you get:

[ \text{Average rate of change} = \frac{h(1) - h(0)}{1 - 0} ]

Now, substitute the values:

[ h(1) = 1^3 - \frac{1}{5}e^1 ] [ h(0) = 0^3 - \frac{1}{5}e^0 ]

Calculate these values and substitute them into the formula to find the average rate of change.

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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 normal line of #f(x)=sqrt(2x^2-x)# at #x=-1#?
- What is the equation of the line normal to #f(x)= x^3+4x^2 # at #x=1#?

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