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Average Values & Other Antiderivative Applications

Average Values & Other Antiderivative Applications. Lesson 7.1. Average Value of a Function. Consider recording a temperature each hour and taking an average If we take it more often and take a limit …. Average Value of a Function. Now apply the concept to a continuous function. f(x). a.

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Average Values & Other Antiderivative Applications

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  1. Average Values & Other Antiderivative Applications Lesson 7.1

  2. Average Value of a Function • Consider recording a temperature eachhour and taking an average • If we take it more often and take a limit …

  3. Average Value of a Function • Now apply the concept to a continuous function f(x) a b

  4. Application • A 20,000 L water tank takes 10 min. to drain. After t min the water left in the tank is V(t) = 200(100 – t2) • What is the average amount of the water in the tank while it is draining?

  5. Root Mean Square • Used to calculate the effective current and effective voltage of alternating current • Root mean square

  6. Root Mean Square • If current is given by • What is the effective current for the time interval from 0 < t < 4

  7. Current and Power • Current, i defined as the time rate of change of the charge, q • Given in coulombs • Passing through a given point in the circuit • Total charge transmitted in a circuit • Voltage between terminals of capacitor with C farads

  8. Current and Power • An 80-μF capacitor is charged to 100 V. It is then supplied a current of i=0.04t3 A. • After what time interval does the capacitor voltage reach 225 V?

  9. Any one of these can be substituted in to the formula above Work • Work expended in an electrical system given by • W in joules • P in watts • Instantaneous power represented by

  10. Work • The power of a certain electrical system is charged according to • What is the formula for energy in this circuit?

  11. Assignment • Lesson 7.1 • Page 262 • Exercises 1 – 31 odd

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