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**Section 5.2 Accumulation Functions**

MAT 213 Brief Calculus Section 5.2 Accumulation Functions

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**The Accumulation Function F(x)**

The accumulation function of a function f(t) , gives the accumulation of the area between the horizontal axis and the graph of f from a to x. The constant a is referred to as the starting value of the accumulation.

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**The Accumulation Function F(x)**

Example , find F(2), F(0), F(-3).

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**The Accumulation Function F(x)**

Example , find F(2), F(0), F(-3). * The value of the accumulation function at the starting point a is zero.

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**The Accumulation Function F(x)**

The accumulation function of a function f(t) is How are F and f related??? f(t) is measured in dollars per day where t is # days after Jan. 1. What are the units on g(t) is measured in miles per hour where t is the number of hours driving. What are the units on

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**The Accumulation Function F(x)**

The accumulation function of a function f(t) is, How are F and f related??? f is the rate of change of F f(x) = F’(x)

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**Sketching Accumulation Graphs**

The graph of a function f(t) is given below. Sketch the following: f(t) 4 2 -1 -2 -4 Tip: Sketch the graph first then shift it up or down if needed.

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**Sketching Accumulation Graphs**

The graph of a function f(t) is given below. Sketch the following: f(t) -1

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