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103年 - 103 國立中山大學轉學生招生考試試題_應數系二年級：微積分#116874

科目：研究所、轉學考(插大)-微積分 | 年份：103年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (10)

(a) If x2y +y3 = 2 and y(1) = 1. Find y'(1) and yn(1) by implicit differentiation. [10%]
(b) Find all relative extreme values of f(x) = 2x3 -3x2-12x+4. [10%]

(a) Evaluate 6531e0f78f9f2.jpg cos2 x sin x dx. [10%]

(b) Evaluate 6531e130676dc.jpg dx. [10%]

(a) Find the interval of convergence of 6531e1a49281f.jpg. [10%]
(b) Find the sum in (a) for x inside the interval of convergence. [10%]
(a) Find the shortest distance from the point (2,0, 1) to the plane x+y+z=1.[10%]
(b) Find the maximum and minimumn values of f(x, y, z) = 2x +y+z+4 subject to the constraint x2 + y2 + z2=6.[10%]

(a) Evaluate the triple integral ∫∫∫Ω(x + 2z)dV, where Ω=(x,y,z)|0≤x,0≤y，1≤x2+y2+z2≤4}[10%]

(b) Evaluate the line integral ∫c(y dx -xdy), where C is the curve x= t2, y=et2, 0≤t≤ 1,from (0,1) to (1,e). [10%]