108年 - 108 國立臺北大學日間學士班轉學生招生考試_統計學系日間學士班二年級：微積分#116784

(a) (7%) Show that f is continuous at 1.

(a)(6%) Let . Find ,where x＞0.

(b) (7%)Let f(x)=x³+x+1. Find (f^-1)'(3).

(c) (7%) Find

(a) (5%) Find the level curve of f(x,y)=0.

(b) (7%) Find ∇f(1,-2), the gradient of f(x,y) at(1,-2).

(c) (8%) Show that f_xx(x,y)+f_yy(x,y)=0.

(a)(8%)

(b)(7%)

(c) (8%) , where R is the region bounded by y=x²and y=.

(d)(7%) ,where R={(x)R²Ix²+y²≤1} .