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Day38-1432class - Math 1432 Register for Test 3 No Class...

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Math 1432 Register for Test 3 No Class Monday – Work the review posted as blank slides then check your work using the “lecture” notes. THINK: The same three letter word can be inserted into each of these words to give a longer word in each case. REED OUTS BRICKING PING FED MISS DEED BEING SING SPED What is the word?
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Notes for series “growth”: Let p(k) be a polynomial in k. r k for r > 1 grows much faster than p(k) k! grows much faster than r k , p(k) k k grows much faster than the others Hence, ( 29 ( 29 ( 29 k k k k k k p k p k p k k r k r r k k k k , , ! ! , , ! ALL converge rapidly.
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Section 11.7 Power Series
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Suppose that ( 29 = - 6 x 1 x f . If you divide 1 – x into 6, you get a “polynomial” that continues forever. ( 29 = + + + + + 2 3 4 P x 6 6x 6x 6x 6x ... This result is a power series. The word series indicates that there is an infinite number of terms. The word power tells us that each term contains a power of x. The series is also a geometric series, with |r|=x, so the series will converge for |x|<1.
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By comparing the graphs of ( 29 = - 6 x 1 x f and P(x) with more and more terms, you will see that between - 1 and 1 (the interval of convergence), the two graphs converge.
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