[數撚圍爐區] What is Mathematics? (4)

unique?

probably not

岩岩發現龜仔未係過呢度留言

啲theorem 成日用induction,但我完全sense 唔到可以用MI

成日做到一半就寫 we will proceed by induction and since it will be obvious from here onwards we will omit the nuisance steps QED

通常見到D for all n, 又似乎有D recursion(?) 就試下用MI

有D MI狠毒係base case最難證

use implicit differentiation to find an equation of the tangent line to hyperbola x^2/6 - y^2/8=1 at x=3
唔識做

assume y is a function of x

有2條tangent lines at x=3, 點解會寫the tangent line

我點知

calculus d 人本身都寫得鳩鳩地架啦
會寫find the parametrisation of blah blah blah, 但明明有無限種parametrisation
d set ge 符號又亂鳩咁寫

我上網睇example係d左舊(x^2/6) - (y^2/8) 再sub返個x落去
但我跟住做完出嚟完全唔覺得係岩 而且根本唔知自己做緊乜
有冇巴打救下我 好趕

Post 上嚟睇下做成點

當年份功課要證Every tree has a centre consisting of either one vertex or two adjacent vertices.

完全無方向，睇solution 見佢用MI

走投無路試下MI無壞

use implicit differentiation to find an equation of the tangent line to hyperbola x^2/6 - y^2/8=1 at x=3
唔識做

assume y is a function of x

我上網睇example係d左舊(x^2/6) - (y^2/8) 再sub返個x落去
但我跟住做完出嚟完全唔覺得係岩 而且根本唔知自己做緊乜
有冇巴打救下我 好趕

(1/6)2x-(1/8)(2y•dy/dx)=0

dy/dx=(x/3) / (y/4)

Since x=3, (1/8)y^2= 3^2/6-1 = 1/2
y= 2 or -2

Then find dy/dx at (3,2) and (3,-2)

Use point-slope form to find equation of st.line

遇到過