2.06.4.Literacy - Accumulation Authors Bill Davis Horacio...

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Accumulation Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 2.06 More Tools and Measurements: Techniques for Calculating Integrals LITERACY What you should be able to handle away from the machine. · L.1) Give a formula for the solution y @ x D of the differential equation y £ @ x D = 0.4 y @ x D with y @ 0 D = 8. · L.2) Give a formula for the solution y @ x D of the differential equation y £ @ x D = x 3 y @ x D with y @ 0 D = 1. · L.3) Why won't the method of separation of variables and integrating work to obtain a formula for y @ x D given y £ @ x D = x 2 y @ x D + 4 Sin @ x D with y @ 0 D = 3? · L.4) Use separation of variables to derive the formula y @ x D = k e rx for a function y @ x D solving y £ @ x D = r y @ x D with y @ 0 D = k. · L.5) Comment on the quotation: "The derivative does not display its full strength until it is allied with the integral." Michael Spivak · L.6) Calculate the following by integration by parts:
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