103年 - 103 國立臺北大學學士班暨進修學士班轉學生招生考試試題_統計學系、經濟學系學士班暨進修學士班二、三年級：微積分#116859

科目：研究所、轉學考(插大)-微積分 | 年份：103年 | 選擇題數：0 | 申論題數：12

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (12)

(a) (9%) Find the Taylor series for f(x) at 1.

(b) (6%) Approximate by P₄(x), the 4^th Taylor polynomial for f(x) at 1.

(a) (6%) Determine whether f is continuous at 1 or not, and justify your answer as well.

(b) (9%) Determine whether f is differentiable at x=0 or not, and justify your answer as well.

3. (20%) Find the relative extrema and saddle points of f(x,y)=3x²y+2y³-3xy.

(a) (6%)

(b)(7%)

(c)(7%) f(x)=e^2xsec²x

(a) (5%)

(b)(7%)

(c) (0%%) . R: the region bounded by y=x and y=

(e) (9%) ， R: the region bounded by