# applied project

## 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.14.7 - Designing a dumpster

Applied Project in Sec.14.7, Calculus by Stewart Chinese version 設計垃圾桶 For this project we locate a rectangular trash Dumpster in order to study and describe all its shape and construction. We then attempt to determine the dimensions of a container of similar design that minimize construction cost. Question 1 : First locate a trash dumpster in your area. Carefully study and describe all details of its

## Sec.14.7 - 設計垃圾桶

Applied Project in Sec.14.7, Calculus by Stewart English version Designing a dumpster 在這個專題中，我們先測量出一個長方體垃圾桶出他的外型和結構。希望設計出一個和它一樣大的容器，並將所需的花費最小化。 問

## Sec.3.5 - Families of Implicit Curves

Applied Project in Sec.3.5, Calculus by Stewart Chinese version 隱式曲線集合 In this project you will explore the changing shapes of implicitly defined curves as you vary the constants in a family, and determine which features are common to all members of the family. Question 1 Consider the family of curves $$y^2-2x^2(x+8)=c[(y+1)^2(y+9)-x^2]$$ (a) By graphing the curves with $c=0$ and $c=2$ , determine how

## Sec.3.5 - 隱式曲線集合

Applied Project in Sec.3.5, Calculus by Stewart 英文版請見 Families of Implicit Curves 在這個專題中你將會發現，若你改變一個隱式曲線集合中的常數，它的形狀會如何改變，並決定集合中的成員會有哪些共同

## Sec.15.8 - Roller Derby

Applied Project in Sec.15.8, Calculus by Stewart Chinese version 滾動競賽 Suppose that a solid ball(a marble), a hollow ball (a squash ball), a solid cylinder (a steel bar), and a hollow cylinder (a lead pipe) roll down a slope. Which of these objects reaches the bottom first? To answer this question, we consider a ball or cylinder with mass $m$, radius $r$, and moment of inertia $I$

## Sec.15.8 - 滾動競賽

Applied Project in Sec.15.8, Calculus by Stewart 英文版請見 Roller Derby 假設有一實心圓球(如一顆彈珠)、一空心圓球 (如一顆壁球)、一實心圓柱(如一根鋼條)、與一空心圓柱(如一根鉛管)同

## 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.13.4 - Kepler’s Laws

Applied Project in Sec.13.4, Calculus by Stewart Chinese version 克卜勒定律 Johannes Kepler stated the following three laws of planetary motion on the basis of massive amounts of data on the positions of the planets at various times. Kepler’s Laws A planet revolves around the sun in an elliptical orbit with the sun at one focus. The line joining the