Imahluko Yezibalo, Izinombolo Zamadijithi, kanye Nokucacisa

Ukwahluka kwesibalo, inani lamadijithi asetshenzisiwe esibalweni esingaphakathi, kanye nesibalo esinembile kuzoya ngohlobo lwesibalo osenzayo.

Umkhawulo Nokunemba Kokubala

Umkhawulo Wokubala	±1 × 10-99 kuya ±9,999999999 × 1099 noma 0
Inani Lemivo Ekubaleni Kwangaphakathi	Imivo engu-15
Ukunemba	Ngokuvamile, ±1 emuvweni we-10 ekubaleni okukodwa. Ukunemba embukisweni ongumphindwa kungu ±1 emuvweni obaluleke kancane kunayo yonke. Amaphutha ayanqwabelana ezibalweni ezilandelanayo.

Ukubala Amafankshini Imikhawulo Yokufakwayo Nokunemba

Amafankshini	Umkhawulo Wokufakwayo
sinx cosx	Deg	0 ≦ \|x\| < 9 × 109
	Rad	0 ≦ \|x\| < 157079632,7
	Gra	0 ≦ \|x\| < 1 × 1010
tanx	Deg	Kuyafana no-sinx, ngaphandle uma u-\|x\| = (2n-1) × 90.
	Rad	Kuyafana no-sinx, ngaphandle uma u-\|x\| = (2n-1) × π/2.
	Gra	Kuyafana no-sinx, ngaphandle uma u-\|x\| = (2n-1) × 100.
sin-1x, cos-1x	0 ≦ \|x\| ≦ 1
tan-1x	0 ≦ \|x\| ≦ 9,999999999 × 1099
sinhx, coshx	0 ≦ \|x\| ≦ 230,2585092
sinh-1x	0 ≦ \|x\| ≦ 4,999999999 × 1099
cosh-1x	1 ≦ x ≦ 4,999999999 × 1099
tanhx	0 ≦ \|x\| ≦ 9,999999999 × 1099
tanh-1x	0 ≦ \|x\| ≦ 9,999999999 × 10-1
logx, lnx	0 < x ≦ 9,999999999 × 1099
10x	-9,999999999 × 1099 ≦ x ≦ 99,99999999
ex	-9,999999999 × 1099 ≦ x ≦ 230,2585092
√x	0 ≦ x < 1 × 10100
x2	\|x\| < 1 × 1050
x-1	\|x\| < 1 × 10100; x ≠ 0
3√x	\|x\| < 1 × 10100
x!	0 ≦ x ≦ 69 (x yinombolo ephelele)
nPr	0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r bayizinombolo eziphelele) 1 ≦ {n!/(n-r)!} < 1 × 10100
nCr	0 ≦ n < 1 × 1010, 0 ≦ r ≦ n (n, r bayizinombolo eziphelele) 1 ≦ n!/r! < 1 × 10100 noma 1 ≦ n!/(n-r)! < 1 × 10100
Pol(x; y)	\|x\|, \|y\| ≦ 9,999999999 × 1099 √x2 + y2 ≦ 9,999999999 × 1099
Rec(r; θ)	0 ≦ r ≦ 9,999999999 × 1099 θ: Kuyafana no-sinx
°’ ”	a°b’c”: \|a\|, b, c < 1 × 10100; 0 ≦ b, c Inani lemizuzwana linephutha elingu ±1 endaweni yesibili yedesimali.
°’ ”←	\|x\| < 1 × 10100 Idesimali ↔ Ukuguqulela i-Sexagesimal 0°0’0” ≦ \|x\| ≦ 9999999°59’59”
xy	x > 0: -1 × 10100 < ylogx < 100 x = 0: y > 0 x < 0: y = n, ^m_{2n + 1} (m, n bayizinombolo eziphelele) Nokho: -1 × 10100 < ylog \|x\| < 100
x√y	y > 0: x ≠ 0, -1 × 10100 < 1/x logy < 100 y = 0: x > 0 y < 0: x = 2n+1, ^{2n + 1}_m (m ≠ 0; m, n bayizinombolo eziphelele) Nokho: -1 × 10100 < 1/x log \|y\| < 100
a b/c	Isamba senombolo ephelele, inombolo engenhla eqhezwini, nenombolo engezansi eqhezwini kumelwe sibe imivo engu-10 noma ngaphansi (sekuhlangene nophawu lokuhlukanisa).
RanInt#(a; b)	a < b; \|a\|, \|b\| < 1 × 1010; b - a < 1 × 1010
GCD(a; b)	\|a\|, \|b\| < 1 × 1010 (a, b bayizinombolo eziphelele)
LCM(a; b)	0 ≦ a, b < 1 × 1010 (a, b bayizinombolo eziphelele)

Ukunemba kuyafana nalokho okuchazwe ngaphansi kwesithi "Umkhawulo Nokunemba Kokubala", ngenhla.

xy, x√y, 3√ , x!, nPr, nCr idinga ukubala kwangaphakathi okulandelanayo, okungenza ukuthi amaphutha enzeka esibalweni ngasinye anqwabelane.

Iphutha liyanqwabelana bese liba into enkulu endaweni lapho kwenzeka khona i-inflekshini.

Umkhawulo wemiphumela yokubala ongavezwa ngesimo sika π uma usebenzisa Isimo Sobuso Semvelo ungu-|x| < 106. Nokho, phawula ukuthi iphutha lokubala elenzeka ngaphakathi lingenza ingaveli eminye imiphumela ngesimo sika-π. Lingabangela nokuba imiphumela yokubala obekufanele ivele ngesimo sedesimali, ivele ngesimo se-π.