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Math 155 Final A to C

# Math 155 Final A to C - Math 155 Section 02 Calculus II...

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Math 155 Section 02 Calculus II Final—Take Home (Last Name: A–C) Name: __________________, ___________________ ID: ____________ Last (print) First (print) (last 4 digits of SSN) 1. Binomial Series [12] a) Expand (4 a – ½ b ) 4 . [3] b) Expand (2 + x ) 2/3 as a power series. Include the term containing x 3 before using the ellipsis (…). [6] c) Approximate 1.9 2/3 using quadratic approximation. (Hint: use answer from part (b) and check your answer with your calculator.) [3] 2. Taylor Series [10] a) Find the Taylor series for ln (2 x + 1) centered at x = 3. Include the term containing ( x – 3) 3 before using the ellipsis (…). [8] b) If 1 2 2 )] 1 2 [ln( + = + x x dx d , find the Taylor series for 1 2 2 + x centered at x = 3. Include the term containing ( x – 3) 2 before using the ellipsis (…). (Hint: use answer from part (a).) [2]

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3. Area Bounded by Two Polar Regions [10] a) Give the polar equations of the two congruent circles shown on the right, Circle 1: r = ________ Circle 2:
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Math 155 Final A to C - Math 155 Section 02 Calculus II...

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