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 write if for any ε > 0 there exists δ > 0 such that

The function f in the figure satisfies Determine all values of d 7 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 < x - 2 < δ

d. |f(x) - 1| < 1 whenever 0 < x - 2 < δ

Transcribed Image Text:

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