100年 - 100 東吳大學轉學生(含進修學士班轉學生)招生考試試題_數學系二年級：微積分#116651

科目：研究所、轉學考(插大)-微積分 | 年份：100年 | 選擇題數：0 | 申論題數：13

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所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (13)

a. the definition of limx→-xo f(x) = L.

b. the fundamental theorem of calculus.

a.

b.

a. Find f'(x) and g'(x) for x≠ 0.

b. Show that f is continuous at 0 but not differentiable there, and that g is differentiable at 0.

c. Show that g' is not continuous at 0.

a.

b.

C.

d.

5. (15%) Find the Taylor expansion of g(x) = In(1+2x) in powers of x=1, and find the interval of convergence of the expansion.

6. (15%) Sketch the polar curve r = 1 - cosθ, 0≤ θ≤π, and calculate the length of the curve.