Suppose X CR, a E X', f: X → R, lim f(x) = L, and c E R is a constant. Prove x-a lim c. f(x) = cL by applying the theorem that lim f(x) = L iff lim f(x) = L when- x-a x-a 7-8 ever (an) is a sequence in X converging to a with an a for all n.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.3: Geometric Sequences
Problem 52SE: Use explicit formulas to give two examples of geometric sequences whose 7thterms are 1024.
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Suppose XC R, a € X', ƒ : X → R, lim f(x) = L, and c € R is a constant. Prove
f
x→a
lim c. f(x) = cL by applying the theorem that lim f(x) = L iff lim f(x) = L when-
x→a
x→a
71-00
ever (Tn) is a sequence in X converging to a with an ‡ a for all n.
Transcribed Image Text:Suppose XC R, a € X', ƒ : X → R, lim f(x) = L, and c € R is a constant. Prove f x→a lim c. f(x) = cL by applying the theorem that lim f(x) = L iff lim f(x) = L when- x→a x→a 71-00 ever (Tn) is a sequence in X converging to a with an ‡ a for all n.
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