106年 - 106 國立臺北大學學士班暨進修學士班轉學生招生考試_統計學系二、三年級：微積分#116786

科目：研究所、轉學考(插大)-微積分 | 年份：106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) (7%) Find .

(b) (5%) Is f continuous at 0 ? Explain your answer as well.

(c) (8%) Is f differentiable at 0 ? Explain your answer as well.

(a) (7%) Find the Taylaor Series for f(x) centered at 1.

(b) (8%) Find the interval of convergence of the power series in (a).

(c) (5%) Find the value of the infinite series.

(d) (5%) Approximate In(1.1) by the 4^th Taylaor Polynomial for f centered at 1.

(a) (6%)

(b)(6%)

(c)(8%)

(a) (5%) Find the equation of C.

(b) (7%) Find the equation the tangent line at the point on level curve C.

(c) (8%) At the point

on the level C what is the direction of the greatest rate of increasing of f(x,y)?

5. (15%) EvaluatedA, where R is the region bounded by x=1, x=3, xy=1, and xy=4.