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Let x > 1, f be continuous and g be a Lipschitz function with constant L satisfying g(1) = 0 defined on the interval [1, x]. Show then that %3D dt f(s)ds If g(x) is continuously differentiable on the interval [1, x], then [g'(t)| < L and it follows by integration by parts that + x which implies immediately the above inequality, where F(t) = f(s)ds. This observation would be a good hint.

Let x > 1, f be continuous and g be a Lipschitz function with constant L satisfying g(1) = 0 defined on the interval [1, x]. Show then that %3D dt f(s)ds If g(x) is continuously differentiable on the interval [1, x], then [g'(t)| < L and it follows by integration by parts that + x which implies immediately the above inequality, where F(t) = f(s)ds. This observation would be a good hint.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Let x > 1, f be continuous and g be a Lipschitz function with constant L satisfying g(1) = 0 defined on the interval [1, x]. Show then that %3D f(t)8(÷) dt|< Lx dt f(s)ds 12 If g(x) is continuously differentiable on the interval [1, x], then |g'(t)| < L and it follows by integration by parts that + x which implies immediately the above inequality, where F(t) = f(s)ds. This observation would be a good hint.
Transcribed Image Text:Let x > 1, f be continuous and g be a Lipschitz function with constant L satisfying g(1) = 0 defined on the interval [1, x]. Show then that %3D f(t)8(÷) dt|< Lx dt f(s)ds 12 If g(x) is continuously differentiable on the interval [1, x], then |g'(t)| < L and it follows by integration by parts that + x which implies immediately the above inequality, where F(t) = f(s)ds. This observation would be a good hint.
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