109年 - 109 國立臺灣大學轉學生招生考試試題_(商、管、農、經學院聯招) ：微積分(C)#113209

1.=?

2. Find f'(2) if f(x)= and g(x) =

3. Trochoid x = 20 - sinθ, y = 2 - cosθ. Find the tangent line of the curve at θ = .

4. Trochoid x = 2θ - sinθ, y = 2 - cos θ. Find the area under the curve and above the x-axis for 0≤θ≤2π.

7. Evaluate where R is the trapezoidal region with vertices (1,0), (2,0), (0,2) and (0,1).

9. Find the absolute maximum value and absolute minimum value of f(x,y) =x⁴+y⁴ -4xy + 1 on the disk x²+y²≤1.

10. Solve the differential equation xy' = y + x² sin x with y(π) = 2π.