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、通訊工程學系日間學士班二年級：微積分#118653

(a)∫x²e^xdx(10%)

(b) ∫xe^{x^2}dx (10%)

(c) (15%)

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

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

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

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