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"Using Definition 6.3.6 Prove the following statement Let f and g be real-valued functions defined on (a, ). Suppose that lim f(x) = L and lim g(r) = M where L, M E R. Then lim (fg)(x) = LM. Let f: (a, x) → R. We say that Le R is the limit of f as x0, and we write 6.3.6 DEFINITION

"Using Definition 6.3.6 Prove the following statement Let f and g be real-valued functions defined on (a, ). Suppose that lim f(x) = L and lim g(r) = M where L, M E R. Then lim (fg)(x) = LM. Let f: (a, x) → R. We say that Le R is the limit of f as x0, and we write 6.3.6 DEFINITION

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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"Using Definition 6.3.6 Prove the following statement Let f and g be real-valued functions defined on (a, ). Suppose that lim f(x) = L and lim g(x) = M where L, M E R. Then lim (fg)(x) = LM. 6.3.6 DEFINITION Let f: (a, 0) → R. We say that Le R is the limit of f as x→ o, and we write lim f(x) = L, provided that for each &>0 there exists a real number N> a such that x > N implies that | f(x) – L| < ɛ.
Transcribed Image Text:"Using Definition 6.3.6 Prove the following statement Let f and g be real-valued functions defined on (a, ). Suppose that lim f(x) = L and lim g(x) = M where L, M E R. Then lim (fg)(x) = LM. 6.3.6 DEFINITION Let f: (a, 0) → R. We say that Le R is the limit of f as x→ o, and we write lim f(x) = L, provided that for each &>0 there exists a real number N> a such that x > N implies that | f(x) – L| < ɛ.
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