Let f : D → R and let c ∈ D. Mark each statement True or False. Justify each answer.(a) f is continuous at c iff for every ε > 0 there exists a δ > 0 such that | f (x) − f (c) | ∈ D.(b) If f (D) is a bounded set, then f is continuous on D.(c) If c is an isolated point of D, then f is continuous at c.(d) If f is continuous at c and (xn) is a sequence in D, then xn → c whenever f (xn) → f (c).(e) If f is continuous at c, then for every neighborhood V of f (c) there exists a neighborhood U of c such that f (U ∩ D) = V.

Let f : D → R and let c ∈ D. Mark each statement True or False. Justify each answer. (a) f is continuous at c iff for every ε > 0 there exists a δ > 0 such that | f (x) − f (c) | ∈ D. (b) If f (D) is...

Let f : D → R and let c ∈ D. Mark each statement True or False. Justify each answer.

(a) f is continuous at c iff for every ε > 0 there exists a δ > 0 such that | f (x) − f (c) | <><>∈ D.

(b) If f (D) is a bounded set, then f is continuous on D.

(d) If f is continuous at c and (x_n) is a sequence in D, then x_n
→ c whenever f (x_n) → f (c).

(e) If f is continuous at c, then for every neighborhood V of f (c) there exists a neighborhood U of c such that f (U ∩ D) = V.

May 05, 2022