Suppose C 1 , C 2 , C 3 , is a nondecreasing sequence of sets, i e , C k C k 1 , for k 1, 2, 3, Then lim k C k is defined as the union C 1 C 2 C 3 Find lim k C k if (a) C k x 1 k x 3 1 k , k 1, 2, 3, (b) C k (x, y) 1 k x 2 y 2 4 1 k , k 1, 2, 3,

Question: Suppose C 1 , C 2 , C 3 , . . . is a nondecreasing sequence of sets, i.e., C k C k+1

Suppose C₁, C₂, C₃, . . . is a nondecreasing sequence of sets, i.e., C_k ⊂ C_k+1, for k = 1, 2, 3, . . . . Then lim_k→∞ C_k is defined as the union C₁ ∪C₂ ∪C₃∪· · ·. Find lim_k→∞ C_k if

(a) C_k= {x : 1/k ≤ x ≤ 3 − 1/k}, k = 1, 2, 3, . . . .

(b) C_k = {(x, y) : 1/k ≤ x² + y² ≤ 4 − 1/k}, k = 1, 2, 3, . . . .

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