triangulum ABC AB , BC 之 circle ニヨル。 T.theodor 2022.8.16 ,

(0,0) カラ ellipse、ellipse 之中心点之回転之 Trajectoriam 、aria ヲ求メヨ。 T.theodor 2022.8.16

ellipse x2/m2+y2/n2 = r2/m2 T.theodor 2022.8.16

y = ax2+bx+c 90°Rotational y = ±√x+b/2a ∓ b2−4ac/4a T.theodor 2022.8.16

hyperbola x2−y2 = r2 vertex (r,0) , (−r,0) focus (√2r,0) , (−√2r,0) T.theodor 2022.8.16

ellipse x2 /a2 + y2 /b2 = 1 hyperbola −(x2 /a2 +y2 /b2 ) = 1 T.theodor 2022.8.15

ellipse circumference of ellipse 之 quarta pars point ヲ求メヨ。 T.theodor 2022.8.15

f(x) = α>β>γ…>ω α= -b+√ b2-4ac /2a2a β= -b-√ b2-4ac /2a2a γ= -b-3√ b2-4ac /2a2a ： ： ω= -b+(n-4)√ b2-4ac /2a2a T.ttheodor 2022.8.15

lim f(x) / g(x) f(x) = αxa+βxa-1+… +ω g(x) = α'xb+β'xb-1+… +ω' a>b lim f(x) / g(x) = ∞ (x→∞) a=b lim f(x) / g(x) = α / α' (x→∞) a

circle x2+y2 = r2 focus ( 2√√r2-x2p -x , p ) directrix y = -p T.theodor 2022.8.14

lim f(x) / g(x) f(x) = αxa+βxa-1+… +ω g(x) = α'xb+β'xb-1+… +ω' a>b lim f(x) / g(x) = ∞ (x→∞) a=b lim f(x) / g(x) = α / α' (x→∞) a

Inequality of arithmetic and geometric means x1 = x2 = · · · = xn. x+y/2 ≧ √ xy x+y+z/3 ≧ 3√ xyz n=2k xn+yn ≧ 2√xnyn ≧ n√xy n=2k-1 xn+yn+zn ≧ 3√xnynzn ≧ n√xyz x1 = x2 = · · · = xn. T.theodor 2022.8.14

lim 1/ ( x→∞ ) T.theodor 2022.8.14

lim n+1√x3+n+2√2x3/22n+1√x5+2n+2√2x5 = ( x→∞ ) T.theodor 2022.8.14

lim ax5+by5/cx5+dy5 (x→∞ , y→∞) T.theodor 2022.8.13

x2/an + y2/bn =1 semi-minor axis n√b2 semi-major axis n√a2 T.theodor 2022.8.12

y = ax+b = a(x + b/a) T.theodor 2022.8.12

f(x) = lim f(x) = axn ( x→0 x<1) lim f(x) = ∞ ( x→∞ ) T.theodor 2022.8.12

y ≧ b2-4ac /44a T.theodor 2022.8.12

f(y) = x = ayn +byn-1 … +z T.theodor 2022.8.11

f(y) = x = ayn +byn-1 … +z T.theodor 2022.8.11

axn + y2 = r2 x2 + ayn = r2 T.theodor 2022.8.11

hyperbola x2 = a2 + a2y2 /b2 /aaaa y = ±b /a √ x2 - a2 = ±b /a √ (x±a)2 ± 2ax - 2a2 T.theodor 2022.8.11

hyperbola x2 = a2 + a2y2 /b2 T.theodor 2022.8.11

AP + BP + CP minimum AP = BP = CP T.theodor 2022.8.10

f(x) = n=2k x = a±b√α, c±d√β,…, t±u√ζ n=2k-1 x = a, b±c√α, c±d√β,…, t±u√ζ T.theodor 2022.8.10

f(x) = an,an-1,…,a0 >0 α,β,…,ω<0 T.theodor 2022.8.10

f(x) = ax3+bx2+cx+d g(x) = ax3 h(x) = bx2+cx+d x = -c±√c2-4bd/ 2b T.theodor 2022.8.9

lim 1/ xn = lim x xi = 1/ xn T.theodor 2022.8.9

lim 1/ x2 = π2 /6n T.theodor 2022.8.9