(a) (8 分)Solve the differential equation 2y' = e^x/2 + y.

1. (10 分) Find the line tangent to the right-hand hyperbola branch defined parametrically by x = sec t, y = tant,-   ＜ t ＜ at point (, 1), where t = π/4.

2. (12 分) A police cruiser (警車), approaching a right-angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 km north of the intersection and the car is 0.8 km to the east, the police determine with radar that the distance between them and the car is increasing at 28 km/hour. If the cruiser is moving at 60 km/hour at the instant of measurement, what is the speed of the car? (See Figure 1)

3. (10 分) How close does the curve y = come to the point (3/2, 0)? (That is, find the minimum distance between the curve and the point. See Figure 2.)

(a) (10 分)Find the length of the curve y = from x = 0 to x = 3.

(b) (10 分)Find the length of the curve given by the polar coordinate equation: r = 8sin³(θ/3), 0 ≤ θ ≤ π/4.

(b) (8 分)Solve the differential equation = x²e4x.

(c) (8 分)Find the solution to = 2xy(y² + 1) that satisfies y(0) = 1.

(a) (6 分)Find.

(b) (6 分)Find .

(c) (6 分)Find f(x) dx where f(x) = 3e(x-ex).

115年 - 115 中央警察大學_碩士班入學考試試題_海洋科技組：微積分#139855

115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所、交通管理研究所：微積分#139760

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題:微積分A#137897

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題：微積分B#137819

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137762

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137761

114年 - 114 國立臺灣大學_轉學生招生考試_物理學系/土木工程學系/生物環境系統工程學系/生物機電工程學系:微積分(B)#137745

114年 - 114 國立臺灣大學_轉學生招生考試_數學系:微積分(A)#137744

113年 - 113 國立嘉義大學_轉學生招生考試試題_(全校)：微積分#122986

112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254