109年 - 109 東吳大學_轉學生招生考試_數學系二年級︰微積分#110884

科目：研究所、轉學考(插大)-微積分 | 年份：109年 | 選擇題數：0 | 申論題數：17

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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 (17)

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3. (8 points) Write down the Taylor series of cos(x) about x = 0.

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(b)

(a) f(x,y) = x sin(xy).

(b) f(x,y)=e⁽^x+y+1),

6. (6 points) Suppose f(x,y, z) = x³y⁴z⁵ and x = sin(t), y = e^t, z = t². Please compute

7. (6 points) Find the directional derivative of f(a, u) = 2my-3y²at the point (x, y) = (5,5) and in the direction u = (4, -3).

8. (8 points) Find all the local maximal, local minimal, and saddle points of the function

f(x,y) =3y²- 2y³ -3x² + 6xy.

9. (8 points) Find the point P = (x, y,z) on the plane 3x -y + 5z -1 = 0 that is closest to (0,0,0).