Explain why or why not Determine whether the following statements are true and give an exp...

Explain why or why not 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.