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'2.7. Assume g e R on [a, b] and define f(x) = Sã g(t) dt if x e [a, b]. Prove that the integral Ig(t)| dt gives the total variation of f on [a, x].

'2.7. Assume g e R on [a, b] and define f(x) = Sã g(t) dt if x e [a, b]. Prove that the integral Ig(t)| dt gives the total variation of f on [a, x].

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.1: Increasing And Decreasing Functions
Problem 44E: Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line...
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'2.7. Assume g e R on [a, b] and define f(x) = Să g(t) dt if x e [a, b]. Prove that the integral S lg(t)| dt gives the total variation of f on [a, x].
Transcribed Image Text:'2.7. Assume g e R on [a, b] and define f(x) = Să g(t) dt if x e [a, b]. Prove that the integral S lg(t)| dt gives the total variation of f on [a, x].
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