104年 - 104 國立臺灣師範大學_學士班轉學生招生考試試題_物理系二年級：微積分#121712

科目：研究所、轉學考(插大)-微積分 | 年份：104年 | 選擇題數：0 | 申論題數：10

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 (10)

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3. (12 分) Find an equation of the tangent line of the curve y = (x+1)^x at the point (1,2).

(a) (12 分) Sketch the graph of the function by finding all asymptotes, interval of increasing and decreasing, and interval of concavity.

(b) (2 分) Show that f(x) ≤ for x ≥ 0.

5. (14 分) Evaluate the indefinite integral ∫tan⁻¹(x) dx as a power series and determine the interval of convergence.

6. (14 分) Find all the local maxima, local minima and saddle points of the function f(x, y) = e^-y(x² + y²).

7. (14 分) Find the volume of the solid bounded above by the surface z = 4 - 4(x² + y²) and below by the surface z = (x² + y²)² - 1.