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Math 1502

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Quiz #2 *

Feb 1

Tom Morley

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Open Book and Notes. Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact.
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Problem 1

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a. Find a series for ln(1-x) (look it up).

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b. Find a series for ln(1-)

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c. Find a series for sin(2x)

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d. Find a series for sin(2 x)

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e. find the limit as x--> 0 of

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Ans

b: Just stubstitute. Everywhere you see an x put an :

c: Start with the series for sin(x), and everywhere you see an x, put an :

d: Multiply the above by :

Look at ratio of leading terms /= -1/2.

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Problem 2 (10 points)

Eddy Merckx Needs to compute an integral. He suggests the folling steps:

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a. From the formula for Taylor series with error bound for (Valid for |x| ≤ 1):

| - ( 1 + x + + + ... + ) | ≤ ,

Derive a formula for Taylor series with error bound for

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b. From the above derive a formula for Taylor series with error bound for

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c. From the above derive a formula for Taylor series with error bound for

b: Now multiply the answer to a: by :

and if you like, simplify:

Integrate b: term by term:

Converted by *Mathematica*
February 1, 2000