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We introduce a sequential divergence criterion for functional limits. We previously proved that the limit of a function f(x) converges to L as x approaches c if and only if f(a_n) converges to L for every a_n converging to c but with terms not equal to c. The contrapositive states that if we can find two sequences a_n and b_n converging to c, but where f(a_n) and f(b_n) do not converge to the same thing - then the limit of f(x) as x approaches c does not exist. #realanalysis
Epsilon-Delta Definition of the Limit of a Function: https://youtu.be/kVQNhAIFZYc
Connecting Function Limits and Sequence Limits: https://youtu.be/7svyCaVjH6w
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