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According to spivak, the defition of limit goes as follows:

" For every ε > 0, there is some δ > 0, such that, for every x, if 0 < |x-a| < δ,

then |f(x) - l |< ε. "

After some exercices, I came across with a doubt.

Say that I could prove that | f(x) - l |< 5ε, for some δ[itex]_{1}[/itex] such that 0 < |x-a| < δ[itex]_{1}[/itex].

Since ε > 0, and thus 5ε > 0, could I say that lim[itex]_{x→a}[/itex]f(x) = l based on this proof?

Regards,

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# Calculus, Definition of limit, Concept

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