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Unformatted text preview: c ∈ ( a,b ) such that f ( p + q +1) ( c ) = 0. 8. Assume that ϕ is a monotonically increasing function and diﬀerentiable. Assume further that for x ≥ x , | f ( x ) | ≤ ϕ ( x ). Prove that for x ≥ x | f ( x )-f ( x ) | ≤ ϕ ( x )-ϕ ( x ) . 9. Page 138: 4, 5, 6, 7, 8 10. Prove Theorem 6.12 on page 128. 11. Assume that α is monotonically increasing and α ∈ R , namely Riemann integrable, on [ a,b ]. Prove that for any bounded function f prove that ¯ Z b a f ( x ) dα = ¯ Z b a f ( x ) α ( x ) dx. 1...
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This note was uploaded on 09/30/2011 for the course MATH 140b taught by Professor Staff during the Winter '08 term at UCSD.
- Winter '08