# Calculus

## 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