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題組內容

第二部分:非題(不需計算過程·答以“F”表示“错”,“T”表示“對”)

(b) Consider two series. Suppose ≥ 0 and . If converges, then converges.

其他申論題

5.The radius of convergence of the power series =__(F)__

6.The Maclaurin serics for sin(x + 1) =__(G)__

(a) If f(x) :=x3 - 2x + 2, x ∈ , then f has a zero between -2 and 0.

(c) If f : (-1,1) → is continuous at x = 0, then f is differentiable at x = 0.

(d) If f : (0,∞)→ (0,∞) is continuous and increasing on (0,∞)； then f(x)=∞.

(e) If f : (0,∞) → is differentiable,i.e., f'(x) exists, , then f'(x) is continuous on .

(f) does not exist.

(g) The series converges.

(h) If converges, then converges.

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