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
這裡我們介紹固定點迭代法 (Fixed point iteration) 首先我們介紹什麼是固定點 (Fixed point) Definition: Fixed point A fixed point of a function $f(x)$ is a number $c$ in its domain such that $f(c)=c$. 所以簡單來說, 把固定點這個數字丟進函數後會
這裡我們要討論一個函數的最大值以及最小值. 首先我們有極值定理 Theorem: Extreme value theorem If $f$ is a real-valued continuous function on the closed interval $[a,b]$, then $f$ must attain a maximum and a minimum. 所以對於定義在封閉區間的連續函
這裡我們要介紹 slant asymptotes, 也就是所謂的斜漸近線. Section 1: slant asymptotes 斜漸近線定義如下: The line $y=mx+b$, $m\ne 0$, is called a slant asymptote of $f(x)$ if $$ \lim_{x\to\infty} [f(x) - (mx+b)] = 0. $$ Remark: 亦可將上列式子中改為 $x\to-\infty$. 滿足此條