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2. Suppose (an) is a sequence of real numbers that converges to 5. Consider the sequences of functions f(x) = x + an and gn(x) = anx. Can we say for sure whether (fn) converges to a limit function on R and whether the convergence is uniform? What about (gn)?

2. Suppose (an) is a sequence of real numbers that converges to 5. Consider the sequences of functions f(x) = x + an and gn(x) = anx. Can we say for sure whether (fn) converges to a limit function on R and whether the convergence is uniform? What about (gn)?

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. Suppose (an) is a sequence of real numbers that converges to 5. Consider the sequences of functions fn(x) = x + an and gn(x) = anx. Can we say for sure whether (fn) converges to a limit function on R and whether the convergence is uniform? What about (gn)?
Transcribed Image Text:2. Suppose (an) is a sequence of real numbers that converges to 5. Consider the sequences of functions fn(x) = x + an and gn(x) = anx. Can we say for sure whether (fn) converges to a limit function on R and whether the convergence is uniform? What about (gn)?
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