Let f : D → R and let c ∈ D. Mark each statement True or False. Justify each answer. (a) If f is continuous at c and c is an accumulation point of D, then lim x →c f (x) = f (c). (b) Every polynomial...

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

(a) If f is continuous at c and c is an accumulation point of D, then lim_{x →c}
f (x) = f (c).

(b) Every polynomial is continuous at each point in
.

(c) If (x_n) is a Cauchy sequence in D, then ( f (x_n)) is convergent.

(d) If f :
 →
 is continuous at each irrational number, then f is continuous on R.

(e) If f :
 →
 and g :
 →
 are both continuous (on
), then f o g and g o f are both continuous on