optimization

Applied Project in Sec.8.3, Calculus by Stewart 英文版請見 Complementary Coffee Cups 假設你選擇了兩種形狀的咖啡杯，一種向外彎曲，另一種向內彎曲，你會注意到它們具有相同的高度，並且形狀可以緊密地貼

Applied Project in Sec.4.1, Calculus by Stewart 英文版請見 The Calculus of ranbows 當陽光照射到半空中的雨滴，光線被散射就會形成彩虹。彩虹自古以來就被人類著迷著，且早在亞里士多德時代以來激發許

Applied Project in Sec.4.1, Calculus by Stewart Chinese version: 彩虹的微積分學 Rainbows are created when raindrops scatter sunlight. They have fascinated mankind since ancient times and have inspired attempts at scientific explanation since the time of Aristotle. In this project we use the ideas of Descartes and Newton to explain the shape, location, and colors of rainbows. Question 1: The figure shows a ray of

Applied Project 2 in Sec.4.7, Calculus by Stewart 英文版請見 Planes and birds: Minimizing energy 像雀科這樣的小鳥滑翔時，會在拍打翅膀和保持翅膀折疊之間進行交替。在這裡，我們觀察這種現象並試著找出鳥類拍

Applied Project in Sec.8.3, Calculus by Stewart Chinese version: Complementary Coffee Cups Suppose you have a choice of two coffee cups of the type shown, one that bends outward and one inward, and you notice that they have the same height and their shapes fit together snugly. You wonder which cup holds more coffee. Of corse you could fill one cup with water and pour it into the other one

Applied Project in Sec.3.1, Calculus by Stewart Chinese version: 建造較佳的雲霄飛車 Suppose you are asked to design the first ascent and drop for a new roller coaster. By studying the photographs of your favorite coasters, you decide to make the slope of the ascent $0.8$ and the slope of the drops $-1.6$. You decide to connect these two straight stretches $y=L_1(x)$ and $y=L_2(x)$

Applied Project 1 in Sec.4.7, Calculus by Stewart 英文版請見 The shape of a can 給定一個體積為 $v$ 的圓柱體罐頭，我們想找到一個高 $h$ 和半徑 $r$ ，將製成罐頭的金屬量減到最小。 如果我們將製程中金

Applied Project 2 in Sec.4.7, Calculus by Stewart Chinese version: 飛機和鳥：能量最小化 Small birds like finches alternate between flapping their wings and keeping them folded while gliding. In this project we analyze this phenomenon and try to determine how frequently a bird should flap its wings. Some of the principles are the same as for fixed-wing aircraft and so we begin by

Applied Project 1 in Sec.4.7, Calculus by Stewart Chinese version: 罐頭的形狀 Given a cylindrical can with fixed volume $v$, we want to find the height $h$ and radius $r$ that minimize the cost of metal to make the can. If we disregard any waste metal in the manufacturing process, then the problem is to minimize the surface area of the cylinder. It can be found that