# HW7 - ≤ 3 Determine which of the following sets are bases...

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MATH 186 – WINTER 2009 HOMEWORK SET 7 Due Friday 03/20 Be kind to your grader, please staple your work! Notice it’s a two-page homework! What you need to know: - Techniques of integrations: by parts, substitution, and partial fractions - Improper integrals - Taylor polynomials - Vector spaces. What you shouldn’t forget: - Deﬁnition of integrable function - Linearly independent vectors and bases. Ex 1. Prove that the improper integral Z 1 2 x + 1 x 2 (1 + x 2 ) dx exists and it’s ﬁnite. Compute it explicitly. Ex 2. Let P 3 be the vector space of the polynomial functions of degree

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Unformatted text preview: ≤ 3. Determine which of the following sets are bases, generating systems (i.e., the set of all their linear combinations generates P 3 ), or linearly independent. i) { 1 ,x,x 3 } . ii) { x + x 3 ,x 2 + 1 ,x 2-1 ,x-x 3 } . iii) { 3 , 1 + x,x + x 2 , 2 x 3 , 3 x + 2 } . 2 MATH 186 – WINTER 2009 HOMEWORK SET 7 From Spivak: Chapter 18: Ex # 31(b)(i) ( ? ) Chapter 19: Ex # 5(viii), 34 Chapter 20: Ex # 1(ii). Please recycle!...
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## This note was uploaded on 11/22/2010 for the course MATH 186 taught by Professor Staff during the Winter '08 term at University of Michigan.

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HW7 - ≤ 3 Determine which of the following sets are bases...

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