Chapter 11: Q1P (page 548)
Sketch or computer plot a graph of the function .
Short Answer
The graph shown is the graph of the function.
Chapter 11: Q1P (page 548)
Sketch or computer plot a graph of the function .
The graph shown is the graph of the function.
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Get started for freeIn Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
7.
In Chapter 1, equations (13.5) and (13.6), we defined the binomial coefficientswhereis a non-negative integer butmay be negative or fractional. Show that can be written in terms offunctions as
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Expand the integrands of Kand E[see ( 12.3 )] in power series in(assuming small k ), and integrate term by term to find power series approximations for the complete elliptic integrals Kand E.
The figure is part of a cycloid with parametric equations (The graph shown is like Figure 4.4 of Chapter 9 with the origin shifted to P2.) Show that the time for a particle to slide without friction along the curve from (x1, y1) to the origin is given by the differential equation for θ(t) is .
Hint: Show that the arc length element is . Evaluate the integral to show that the time is independent of the starting height y1 .
In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
10. .
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