Given the function f(x) = x³ defined on /= [0,1]- Suppose that pis a partition and p' is a refinement of p which adds one more point. Show that: a. Up(f) < Up(f) and Lp(f) > Lp(f) b. Give an example of a function f defined on / such that Up(f) = Up(f) and LprA) = Lp(f) for the two partions in Part (a). c. If f is strictly increasing continuous function on /. Show that Up(f) < Up(f) where pr is any refinement of p.
Given the function f(x) = x³ defined on /= [0,1]- Suppose that pis a partition and p' is a refinement of p which adds one more point. Show that: a. Up(f) < Up(f) and Lp(f) > Lp(f) b. Give an example of a function f defined on / such that Up(f) = Up(f) and LprA) = Lp(f) for the two partions in Part (a). c. If f is strictly increasing continuous function on /. Show that Up(f) < Up(f) where pr is any refinement of p.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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