(Extra credit, 10 points) Assume that f: RR is such that f (x0+x1) = f (x0) f (x1) for all xo, x1 E R. If f has a limit at zero, prove that f has a limit at every point and either L = limo f (x) = 1 or f (x) = 0 for all x E R. [Hint: For the last part, when L = lim x->0 f (x) = 0 (why?), assume that there is a point xo, such that f (x0) the sequence {f(xo/n)}1. What is the limit of this sequence?] 0. Consider
(Extra credit, 10 points) Assume that f: RR is such that f (x0+x1) = f (x0) f (x1) for all xo, x1 E R. If f has a limit at zero, prove that f has a limit at every point and either L = limo f (x) = 1 or f (x) = 0 for all x E R. [Hint: For the last part, when L = lim x->0 f (x) = 0 (why?), assume that there is a point xo, such that f (x0) the sequence {f(xo/n)}1. What is the limit of this sequence?] 0. Consider
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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