105年 - 105 國立臺灣師範大學_學士班二年級轉學生招生考試試題_資訊工程學系：微積分#120313

科目：研究所、轉學考(插大)-微積分 | 年份：105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) (8 points)Find d²y/dx² if x³ - 3y² = 8.

(b) (8 points)Find dy/dx if y=

(a) (8 points)find an equation for the line tangent to the curve at t = -1, and

(b) (8 points)find the value of d²y/dx² at this point.

3.(8 points)Evaluate the integral.

4.(12 points)Solve the equation given the initial condition y(0) = 5.

(a) (6 points)Find .

(b) (10 points)Find the area under the curve y = 2ln(x) / x² from x = 1 to x = ∞.

(a) (8 points)Find the Taylor series generated by f(x) = 1/x at a = 2, and

(b) (4 points)where does the series converge to 1/x?

7.(8 points)Find the value of ∂z/∂x at point (1, 1, 1) if the equation xy + z³x - 2yz = 0 defines z as a function of the two independent variables x and y and the partial derivative exists.

8.(12 points)Find the absolute maximum and minimum values of f(x, y) = 2 + 2x + 2y - x² - y² on the triangular plate in the first quadrant bounded by lines x = 0, y = 0, y = 9 - x.