Quiz5Spr2010 - Does the series converge to sin( x ) on this...

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Honors Calculus II Quiz 5 1. Determine a power series for the function 1 1 ! x centered at a = 3 . What is the radius of convergence and interval of convergence of the series. Does the series converge to 1 1 ! x on this interval? 2. Determine a power series for sin( x ) centered at a = 0 . What is the radius of convergence and interval of convergence for the series.
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Unformatted text preview: Does the series converge to sin( x ) on this interval? Solve the same problem for a = ! 2 . 3. Solve the differential equation dy dx = y ! 1 with initial condition y (0) = 1 using power series. [Hint: Assume y ( x ) = a n x n n = ! " and solve for the coefficients.]...
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