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Answers for “为什么定义要求这对每一个 epsilon 都有效,而不仅仅是一个?”

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To find a delta for a given epsilon, you first identify the target output range (L−ϵ,L+ϵ)(L - \epsilon, L + \epsilon). Then, you examine the graph of the function to find the corresponding input range around aa that maps into this output range.

Conditions: A specific function graph is available.; Values for LL, aa, and ϵ\epsilon are given.; The function is continuous or has a limit at aa.