106年 - 106 國立臺灣師範大學_學士班轉學生招生考試試題_企業管理學系二年級：微積分#121702

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：20

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 (20)

(1) If f(t) ＜ 0, then df/dt ＜ 0 (5 points)

(2) The derivative of (f(t))² is 2 df/dt (5 points)

(3) The derivative of 2f(t) is 2 df/dt (5 points)

(4) The derivative is the limit of Δf divided by the limit of Δt (5 points)

(5) The derivative of |x|³ is 3|x|² (5 points)

(6) tan²x and sec²x have the same derivative (5 points)

(1) Find its average speed Δf/Δt from t = 0 to t = (5 points)

(2) Find its average speed Δf/Δt from t = to t = 1 (5 points)

(3) What is df/dt at t = (5 points)

3. Graph y = x³ + x² - x from x = -2 to x = 2 and estimate where it is decreasing. Check the transition points by solving dy/dx = 0. (5 points)

4. Find solutions (i.e., y equations) to dy/dx = sin 3x and dy/dx = cos 3x. (5 points)

(1) (x + 1)(x - 1) (5 points)

(2) (5 points)

(3) (x - 1)(x - 2)(x - 3) (5 points)

(4) x² cosx + 2x sin x (5 points)

(5)(5 points)

(6) (5 points)

(7) x⁴ + cosx + x cos⁴x (5 points)

(8) x² sin x cos x + sin x (5 points)

(9) sec²x - tan²x (5 points)