Determine whether the following statements are true and give an explanation or counterexample. Assume a and L are finite numbers and assume

a. For a given ε > 0, there is one value of δ > 0 for which |f(x) - L| < ε whenever 0 < | x - a| < δ.

b. The limit means that given an arbitrary δ > 0, we can always find an ε > 0 such that |f(x) - L| < ε whenever 0 < |x - a| < δ.

c. The limit  means that for any arbitrary ε > 0, we can always find a δ > 0 such that |f(x) - L| < ε whenever 0 < |x - a|< δ.

d. If |x - a| < δ, then a - δ < x < a + δ.

Transcribed Image Text:

|lim f(x) = L. x- lim f(x) = L