Suppose (an) is a sequence of real numbers that converges to 5. Consider the sequences of...
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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)? 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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