Let k(x) = h(x) - g(x), where g and h are infinitely differentiable functions from R to R. Define f(n) to be the nth derivative of a function mapping R to R. Suppose hn(x) = gn(x) for all x. Suppose k(x1) = k(x2) = ... = k(xn) = 0 for x1 < x2 < x3 < ... < xn . Show that g = h.
Let k(x) = h(x) - g(x), where g and h are infinitely differentiable functions from R to R. Define f(n) to be the nth derivative of a function mapping R to R. Suppose hn(x) = gn(x) for all x. Suppose k(x1) = k(x2) = ... = k(xn) = 0 for x1 < x2 < x3 < ... < xn . Show that g = h.
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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Let k(x) = h(x) - g(x), where g and h are infinitely
x1 < x2 < x3 < ... < xn . Show that g = h.
Expert Solution
Step 1
Let , where and are infinitely differentiable functions from .
Let be the derivative of a function mapping and .
Suppose for
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