OLD-final2

# OLD-final2 - Calculus For Electronic Engineering and...

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Calculus For Electronic Engineering and Computer Science Final Examination (A)-100 Points (Spring 2010) Department: Major: Number: Name: Score: INSTRUCTIONS: PLEASE WORK ALL 11 PROBLEMS BELOW. NO CALCULATORS, BOOKS, PAPERS, OR NOTES ARE ALLOWED. YOU MUST SHOW YOUR WORK CLEA- RLY TO RECEIVE CREDIT. 1. (8 points) Determine whether the following series is divergent, conditionally convergent or absolutely convergent. ° =1 ( 1) ° ( ° 1 ° 1) . 2. (10 points) Find ∂? ∂? and ∂? ∂? if ? 3 + ? 3 + ? 3 + 6 ??? = 1 .

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? ( ± ) = ? + ? 2 (1 ? ) 3 as a power series centered at ± = 0. State clearly the radius of convergence of the power series. (Hint: use the bi- nomial series.) (2) Use part (1) to ﬁnd the sum of the series ° =1 ° 2 2 ° . 4.(10 points) Find the maximum and minimum values of the following function subjected to the given constraints ? ( ±, ? ) = ± + 2 ? ; ± + ? + ? = 1 , ? 2
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## This note was uploaded on 06/21/2011 for the course CIVIL 1010 taught by Professor Unknown during the Spring '10 term at HKU.

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OLD-final2 - Calculus For Electronic Engineering and...

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