PracticeTest4 - Center: ___________ Rewritten series:...

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Practice Test #4 – MAC2312 Directions: Use this practice test as a guide for your study for Test #4. This exam is not comprehensive, so study your quiz, class notes and homework problems in addition to completing this exam. Solutions are posted on the course website under “Solutions”. 1) Convert the series 1 2 4 2 ) 1 ( 8 n n n into either the form 1 1 n n n a or 1 1 1 n n n a . Show all work. 2) Use the Alternating Series Test to prove that 1 2 1 5 7 ) 1 ( n n n converges. Show all work. 3) Determine if the series in #3 converges absolutely or conditionally. Show all work. 4) Apply an appropriate test to determine if each series converges or diverges. State which test you are using for each. a) 1 4 )! 3 ( ) 3 ( 5 n n n n b) 1 2 2 3 n n n n c) 1 2 7 4 n n Test: ________ Test: ________ Test: ________ 5) Find the third Taylor polynomial centered at -2 to approximate the function 1 3 5 ) ( x e x f . 6) Rewrite 0 )! 5 2 ( ) 4 ( n n n x in power series form, say what the center is, and expand for four terms.
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Unformatted text preview: Center: ___________ Rewritten series: _______________ Expansion: ___________________ 7) Consider the power series 1 7 6 ) ( n n x x f . a) Find the center and radius of convergence (using the Ratio Test). Center: ____________ Radius: ___________ b) How would you find the interval of convergence? Describe the steps without actually finding the interval. 8) If f(x) = 2011 2 n n n x , find and dx x f ) ( . (Hint: Write in power series form first!) = ___________________ = ________________ 9) Rewrite x x f 3 2 ) ( as a power series centered at 11 by first converting into a geometric series. Then, find the radius of convergence. Show all work! Geometric series: ________________ Power series: __________________ Radius of convergence: _________...
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PracticeTest4 - Center: ___________ Rewritten series:...

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