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Assume that f : (0,1) → R is continuous, and (xn), (Yn) C (0,1) are such 1, and lim f(xn) = l, lim f(yn) lim Yn L for some real numbersl< L. that lim xn %3D %3D n00 n00 n-00 Prove that for every A E R such that l < < L there exists (zn) C (0, 1) such that lim zn = 1, and lim f(zn) = .

Assume that f : (0,1) → R is continuous, and (xn), (Yn) C (0,1) are such 1, and lim f(xn) = l, lim f(yn) lim Yn L for some real numbersl< L. that lim xn %3D %3D n00 n00 n-00 Prove that for every A E R such that l < < L there exists (zn) C (0, 1) such that lim zn = 1, and lim f(zn) = .

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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Assume that f : (0,1) → R is continuous, and (xn), (Yn) C (0,1) are such L for some real numbers l < L. that lim xn = lim yn = 1, and lim f(xn) = l, lim f(yn) Prove that for every A E R such that l < < L there exists (z,) C (0, 1) such that lim zn = 1, n→∞ 6. and lim f(zn) = X.
Transcribed Image Text:Assume that f : (0,1) → R is continuous, and (xn), (Yn) C (0,1) are such L for some real numbers l < L. that lim xn = lim yn = 1, and lim f(xn) = l, lim f(yn) Prove that for every A E R such that l < < L there exists (z,) C (0, 1) such that lim zn = 1, n→∞ 6. and lim f(zn) = X.
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