... 1 Suppose that for i = 1,2, m the function fi is real valued on the interval [a, b] of the form that, for every i, there exists a sequence of polynomials that uniformly converges to fi in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to the product function f₁f2 fm on [a, b].
... 1 Suppose that for i = 1,2, m the function fi is real valued on the interval [a, b] of the form that, for every i, there exists a sequence of polynomials that uniformly converges to fi in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to the product function f₁f2 fm on [a, b].
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 58EQ
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![Suppose that for i = 1,2, ..., m the function fi is real valued on the interval [a, b] of the
form that, for every i, there exists a sequence of polynomials that uniformly converges to fi
in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to
the product function f₁f₂ fm on [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd694394d-74eb-4bc1-a118-9109e1a5a9dd%2F879f5108-a022-4a35-8814-625c903a4ffd%2Fmll5dd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that for i = 1,2, ..., m the function fi is real valued on the interval [a, b] of the
form that, for every i, there exists a sequence of polynomials that uniformly converges to fi
in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to
the product function f₁f₂ fm on [a, b].
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