Use the following definitions. Assume f exists for all x near a with x > a. We say the limit of f(x) as x approaches a from the right of a is L and write, if for any ε > 0 there exists δ > 0 such that

Assume f exists for all x near a with x < a. We say the limit of f(x) as x approaches a from the left of a is L and writeif for any ε > 0 there exists δ > 0 such that

Why is the last inequality in the definition
of namely, 0 < |x - a| < δ, replaced with 0 < x - a < δ in the definition of

Transcribed Image Text:

lim f(x) = L, х- хэа || f(x) – L| < ɛ whenever 0 < x – a < 8.