mth.122.handout.13

# mth.122.handout.13 - MTH 122 Calculus II Essex County...

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Essex County College — Division of Mathematics and Physics 1 Lecture Notes #13 — Sakai Web Project Material We won’t ﬁnish this in class, but I do encourage you to continue working on this on your own. You should also try using a graphing utility to graph very high degree polynomial . .. you might learn something! Consider the functions y = e - x 2 and y = 1 1 + x 2 . 1. Write the Taylor expansions for the two functions about x = 0. What is similar about these two series? What is diﬀerent? 2. Looking at the series, which function do you predict will be greater over the interval ( - 1 , 1)? Graph both and see. 3. Are these functions even or odd ? How might you see this by looking at the series expansion? 4. By looking at the coeﬃcients, explain why it is reasonable that the series for y = e - x 2 converges for all values of x , but the series for y = 1 1 + x 2 converges only on ( - 1 , 1). 1

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## This note was uploaded on 01/31/2011 for the course MTH 222 taught by Professor Ban during the Spring '10 term at Essex County College.

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mth.122.handout.13 - MTH 122 Calculus II Essex County...

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