105年 - 105 國立臺北大學日間學士班暨進修學士班轉學生招生考試試題_資訊工程學系、通訊工程學系日間學士班二年級：微積分#116858

(a)∫x²e^xdx(10%)

(b)

(c) (15%) 

(d) ∫∫_D x + 2y dA, where D is the region bounded by the parabolas y = 2x² and y= 1+ x².(15%)

2. Please sketch the curve y =(You must describe the domain, intercepts, symmetry, asymptotes, interval of increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.) (15%)

3. If f(x,y) =- exists? Why?(10%)

5.Find the radius of convergence and interval of convergence of the series .(15%)