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(2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

(2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da

Advanced Engineering Mathematics
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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(2) Show that Vne-na? lim Vne-na? da lim dr n00 for a >0 but not for a = 0. (4) Let f : R → R be a C-function such that f(x) = 0 if and only if x e Z. Suppose the function a : R R satisfies a'(t) =f (x(t)) for all t e R. (a) If Zn{r(t) : t e R} is non-empty, then show that a is constant. (b) If Zn{x(t) : t e R} is the empty set, then show that lim a(t) t+00 exists and is an integer.
Transcribed Image Text:(2) Show that Vne-na? lim Vne-na? da lim dr n00 for a >0 but not for a = 0. (4) Let f : R → R be a C-function such that f(x) = 0 if and only if x e Z. Suppose the function a : R R satisfies a'(t) =f (x(t)) for all t e R. (a) If Zn{r(t) : t e R} is non-empty, then show that a is constant. (b) If Zn{x(t) : t e R} is the empty set, then show that lim a(t) t+00 exists and is an integer.
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