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Calculus I (MAT 145) Dr. Day Fri day , April 12, 2013

Calculus I (MAT 145) Dr. Day Fri day , April 12, 2013. Reversing the Derivative Process—And All the Ramifications of That! Antiderivatives (4.9 and 5.1) The Fundamental Theorem of Calculus! This Week Complete WA 5.1, 5.2, and 4.9 Gateway Quiz #6. Accumulate , Accumulate, Accumulate !.

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Calculus I (MAT 145) Dr. Day Fri day , April 12, 2013

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  1. Calculus I (MAT 145)Dr. DayFriday, April 12, 2013 • Reversing the Derivative Process—And All the Ramifications of That! • Antiderivatives (4.9 and 5.1) • The Fundamental Theorem of Calculus! This Week • Complete WA 5.1, 5.2, and 4.9 • Gateway Quiz #6 MAT 145

  2. Accumulate, Accumulate, Accumulate! How much snow fell? MAT 145

  3. Areas and Distances (Sec 5.1: PIP p 72) • Use What You Know to Get at What You’re Looking For • Choosing Endpoints • Notation • Accumulations From Rates MAT 145

  4. Antiderivatives, Integrals, and Initial Value Problems • Knowing f’, can we determine f ? General and specific solutions: The antiderivative. • The integral symbol: Representing antiderivatives • Initial Value Problems: Transforming a general antiderivative into a specific function that satisfies the given information. MAT 145

  5. If we know a rate function . . . Carlota Music Company estimates that the marginal cost of manufacturing its Professional Series guitars is given by the following in dollars/month when the level of production is x guitars/month: C'(x) = 0.004x + 50. The fixed costs incurred by Carlota are $9000/month. Determine a model for the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month. MAT 145

  6. Approximating Area: Riemann Sums To generate a way to calculate the area under the curve of a rate function, in order to determine an accumulation, we begin with AREA APPROXIMATIONS. We create something called a Riemann Sum and use better and better area approximations that will lead to exact area. MAT 145

  7. Approximating Area: Riemann Sums Riemann Sum Applet MAT 145

  8. The Fundamental Theorem of Calculus (Part II) Let f be continuous on [a, b]. Then, where F is any antiderivative of f; that is, F′(x)= f(x). MAT 145

  9. The Fundamental Theorem of Calculus (Part I) For f continuous on [a, b], let the function gbe Then g(x) is an antiderivative of f: MAT 145

  10. Assignments WebAssign • 5.1 due tonight Also • Next Test: Fri 4/26 • Chapter 5—5.1-5.4 and 4.9; Review Problems • Review Assignments posted to WA MAT 145

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