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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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