# optimization

## Sec.10.3 - 極座標曲線家族

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

## Sec.5.2 - Area functions

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

## Sec.5.2 - 面積函數

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

## Sec.3.1 - 建造較佳的雲霄飛車

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

## Sec.6.5 - Where to Sit at the Movies

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

## Sec.6.5 - 電影院要坐哪?

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

## Sec.11.11 - Radiation From The Stars

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