Precise definitions for left- and right-sided limits Use the following definitions.Assume...

Precise definitions for left- and right-sided limits 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 xthe limit of f (x) as x approaches a from the left of a is L and write , if for any ε > 0 there exists δ > 0 such that

Determining values of δfrom a graph The function f in the figure satisfies  and . Determine all values of δ > 0 that satisfy each statement.

a. |f(x) − 0|<2 whenever 0<x − 2<δ

b. |f(x) − 0|<1 whenever 0<x − 2<δ

c. |f(x) − 1|<2 whenever 0<2 − x<δ

d. |f(x) − 1|<1 whenever 0<2 − x<δ