derivative

Laboratory Project in Sec.10.3, Calculus by Stewart English version: Families of Polar Curves 在這個研究中，你將發現極座標曲線家族有趣又漂亮的形狀。同時，當常數改變時，你也會觀察到曲線形狀的變化。 問題 1: (a) 探討

Discovery Project in Sec.5.2, Calculus by Stewart Chinese version 面積函數 Question 1(a): Draw the line $y = 2t+1$ and use geometry to find the area under this line, above the t-axis, and between the vertical lines $t=1$ and $t = 3$. Answer: let $f(x)=y=2t+1$, then $f(1)=3$ and $f(3)=7$. So, Area$= \frac{1}{2}(3+7)(3-1) = 10$ Question 1(b): If $x>1$, let $A(x)$ be the area of the region that lies

Discovery Project in Sec.5.2, Calculus by Stewart 英文版請見 Area functions Question 1(a): 畫出 $y = 2t+1$ 且用幾何方法找出在此線下方、$t$軸上方、與$t＝1$和$ｔ＝３$兩條垂直線所圍出的面積. Answer: 令 $f(x)=y=2t+1$, 則

Applied Project in Sec.3.1, Calculus by Stewart 英文版請見 Building a better roller coaster 假設你被要求設計一架新的雲霄飛車的第一個上升與下降。在研究你最喜歡的雲霄飛車的圖片後，你決定新的雲霄飛車先

Applied Project in Sec.6.5, Calculus by Stewart Chinese version 電影院要坐哪? A movie theater has a screen that is positioned $3$m off the floor and is $10$m high. The first row of seats is placed $3$m from the screen and the rows are set $1$m apart. The floor of the seating area is inclined at an angle of $\alpha=20^{\circ}$ above the horizontal and the distance

Applied Project in Sec.6.5, Calculus by Stewart English version Where to Sit at the Movies? 有家電影院的螢幕高10米且離地3公尺，第一排的位子距離螢幕3公尺且每排間隔1公尺，座位區的地板以與水平20度夾

Applied Project in Sec.11.11, Calculus by Stewart Chinese version 恆星的輻射 Any object emits radiation when heated. A blackbody is a system that absorbs all the radiation that falls on it. For instance, a matte black surface or a large cavity with a small hole in its wall (like a blastfurnace) is a blackbody and emits blackbody radiation. Even the radiation from the sun is close to

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