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 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
Applied Project in Sec.3.4, Calculus by Stewart Chinese version: 飛行員應該何時開始下降高度? An approach path for an aircraft landing is shown in the figure and satisfies the following conditions: (i) The cruising altitude is $h$ when descent starts at a horizontal distance $\ell$ from touchdown at the origin. (ii) The pilot must maintain a constant horizontal speed $v$ throughout