108年 - 108 國立臺北大學_日間學士班轉學生招生考試試題_統計學系日間學士班2年級：微積分#116784

科目：研究所、轉學考(插大)-微積分 | 年份：108年 | 選擇題數：0 | 申論題數：14

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 (14)

(a) (10%) If f(1)=18 is a relative maximum and f(-3)= -14 is a relative of minimum f, please find f(x).
(b) ( 5%) Find the value of k so that (k, f(k))is a point of inflection of f(x).
(a) (7%) Show that f is continuous at 1.
(b) (8%) Show that f is differentiable at 1. 

(a)(6%) Let 651a22a67d214.jpg. Find 651a22c638cd4.jpg,where x＞0. 
(b) (7%)Let f(x)=x3+x+1. Find (f-1)'(3). 

(c) (7%) Find 651a2332e6122.jpg
(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 fxx(x,y)+fyy(x,y)=0.

 (a)(8%) 651a239c64f4e.jpg

(b)(7%) 651a23dc7423e.jpg

(c) (8%) 651a2404cef2f.jpg, where R is the region bounded by y=x2 and y=651a241f17af6.jpg.

(d)(7%) 651a256c29b7d.jpg,where R={(x)651a2594a2278.jpgR2Ix2+y2≤1} .