3. (10 points) Evaluate |_(0,1) for
u(x,y) = (eˣ - dt.

Note: Answer must in numerical expression and natural constants like π, e, ...etc.

4. (10 points) Evaluate |(2,0) foru(x,y) = h(x² + y², 3x – 4y)whereh(s,t) =

5. (10 points) Find the volume of the solid generated by rotating the curvey = sin(x²)over 0 ≤ x ≤ 1 around the y-axis.

6. (10 points) Evaluate the infinite sumby some manipulations of the Taylor series of f(x) = xeˣ.

7. (10 points) A dog is running along a semi-circular track with radius 1 km incounterclockwise direction with speed 0.1 km per minute (See Figure).Let h be the distance between the dog and point A. Find the rate of change of h at point D, half way between B and C.

8. (10 points) Find (f⁻¹)'(5) forf(x) = x⁵ + 2x³ + 2x.

9. (10 points) Evaluatedydx.

10. (10 points) Use Lagrange multiplier to find the extreme value off(x, y, z) = exyzsubject to the constraintx³ - y² + z³ = 24.Also, indicate the value(s) you obtain is (are) maximum or minimum.

IV. WritingNowadays, communicating online seems to become the norm. People are writing blogs, creating Facebook profiles, sharing videos on YouTube and tweeting on Twitter. In particular, social media has given people the power to share and stay connected； however, social media may also promote negative experiences such as feeling inadequate about your life or appearance. Please write an essay of about 300 words to illustrate how people can minimize the negative effects of social media.

(a) (5 points)

(b) (5 points)

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