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Pomax
2020-10-18 14:27:57 -07:00
parent 133105d44e
commit 0f6683ca6d
314 changed files with 11182 additions and 266 deletions
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
(b-a)t + a= 0,
(b-a)t= -a,
-a
t= ───
b-a

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌────────┐
│ 2
2 -b ±⟍│b - 4ac
Given f(t) = at + bt + c, f(t)=0 when t = ───────────────
2a

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
f (x )
y n
x = x - ───────
n+1 n f' (x )
y n

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
B'(t) = a(1-t) + b(t)= 0,
a - at + bt= 0,
(b-a)t + a= 0

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
a= v -2v +v = 3(-p + 3p - 3p + p )
1 2 3 1 2 3 4
b= 2(v -v ) = 6(p - 2p + p )
2 1 1 2 3
c= v = 3(p -p )
1 2 1

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
B(t) uses { p ,p ,p ,p }
1 2 3 4
B'(t) uses { v ,v ,v }, where v = 3(p -p ), v = 3(p -p ), v = 3(p -p )
1 2 3 1 2 1 2 3 2 3 4 3

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2 2
B'(t)= v (1-t) + 2v (1-t)t + v t
1 2 3
2 2 2
...= v (t - 2t + 1) + 2v (t-t ) + v t
1 2 3
2 2 2
...= v t - 2v t + v + 2v t - 2v t + v t
1 1 1 2 2 3
2 2 2
...= v t - 2v t + v t - 2v t + v + 2v t
1 2 3 1 1 2
2
...= (v -2v +v )t + 2(v -v )t + v
1 2 3 2 1 1

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3 2
very hard: solve at + bt + ct + d = 0
3
easier: solve t + pt + q = 0