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Let R(x) be the remainder of the Taylor expansion of e: e®z" +1 (n + 1)!' R,(x) for some c e (0, z) Show that for any fixed z, lim Rn(x) = 0

Let R(x) be the remainder of the Taylor expansion of e: e®z" +1 (n + 1)!' R,(x) for some c e (0, z) Show that for any fixed z, lim Rn(x) = 0

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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Let R,(x) be the remainder of the Taylor expansion of e": er" +1 R, (x) for some c e (0, x) (n + 1)!' Show that for any fixed x, lim Rn(x) = 0 n+ 00
Transcribed Image Text:Let R,(x) be the remainder of the Taylor expansion of e": er" +1 R, (x) for some c e (0, x) (n + 1)!' Show that for any fixed x, lim Rn(x) = 0 n+ 00
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