Unformatted text preview: . 8 ≤ x ≤ 1 . 2. 5. [10 points] Find the Taylor series centered at a = 2 for the function f ( x ) = e x . 6. [15 points] Use a power series to approximate Z . 5 1 √ 1 + x 3 dx accurate to four decimal places. 7. [10 points] Write an integral for the length of the curve y = cos x with 0 ≤ x ≤ π , but do not evaluate the integral. 8. [10 points] Find the centroid of the region bounded by y = e x , y = 0, x = 0, and x = 1. 9. [10 points] If f ( x ) = e 2 x cos x , use power series to ﬁnd f (4) (0)....
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 Winter '98
 MathDep
 Math, Power Series, Taylor Series, Math 21H Apr.

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