Test4Spr2010 - f ( x ) = ! x ! (1 " x ) for the...

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Name MAC 3473, Honors Calculus 1 Keesling Test 4 4/20/2010 Do all problems. Show your work and explain your answers. Each problem is 20 points. 1. Determine the power series for the following functions. (a) sin( x ) = a n x n n = 0 ! " (b) 1 1 + x 2 = a n x n n = 0 ! " 2. Solve the following differential equation using power series. Solve for the first six coefficients, { a 0 , a 1 , a 2 , a 3 , a 4 , a 5 } , assuming y = a n x n n = 0 ! " . ! y = y + x 2 y (0) = 1
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3. (a) tan 7 xdx ! (b) 1 1 ! 9 x 2 dx " 4. Find the attracting periodic orbit for
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Unformatted text preview: f ( x ) = ! x ! (1 " x ) for the following values of . Give the points in the orbit accurate to ten digits. =3.49856169933 = 3.8318740552833 5. Prove that if f : I ! I is a continuous function on an interval I , and there is a point x ! I which has period three, then there is a point y ! I which has period seven....
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This note was uploaded on 07/14/2011 for the course MAC 3473 taught by Professor Block during the Spring '08 term at University of Florida.

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Test4Spr2010 - f ( x ) = ! x ! (1 " x ) for the...

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