Isibalo samalensi ahlanganayo (ayi-convex)

Isihloko mayelana ne-Equation yamalensi ahlanganayo (convex)

Ngaphambi kokufunda i-equation yelensi eqondile, qonda imithetho yezimpawu zelensi eqondile ngezansi.

Imithetho yesibonakaliso selensi eqondile

- Ibanga lento (do)

Uma into idlula emsebeni wokukhanya, khona-ke ibanga lento unethemba.

- Ibanga lesithombe (di)

Uma ukukhanya kudlula isithombe, khona-ke ibanga lesithombe kuyinto enhle (isithombe sangempela). Uma ukukhanya kungadluli esithombeni, ibanga lesithombe kuyinto engemihle (isithombe esibonakalayo).

- Ubude obuqondile (f)

Uma umsebe wokukhanya udlula endaweni eqondile yelensi, ubude be-focal belensi buyi-positive. Ngokuphambene nalokho, uma umsebe wokukhanya ungadluli indawo eqondile yelensi, ubude be-focal belensi buyi-negative. Indawo eqondile yelensi eqondile idlula endaweni eqondile yokukhanya. Ngakho-ke, ubude be-focal belensi eqondile buyi-positive.

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- Ukuphakama kwento (ho)

Uma into ingaphezu kwe-axis eyinhloko, khona-ke ukuphakama kwento kusayinwe kukuhle (into iqondile). Ngokuphambene nalokho, uma into ingaphansi kwe-axis eyinhloko yelensi eqondile, ukuphakama kwento kukubi (into iguquliwe).

- Ukuphakama kwesithombe (hi)

Uma isithombe singaphezu kwe-axis eyinhloko, ukuphakama kwesithombe kuqondile (isithombe siqondile). Uma isithombe singaphansi kwe-axis eyinhloko, ukuphakama kwesithombe kuphambene (isithombe siphendukezelwe).

- Ukukhulisa isithombe (m)

Uma ukukhulisa isithombe > 1, khona-ke usayizi wesithombe mkhulu kunosayizi wento. Uma ukukhulisa isithombe = 1, khona-ke usayizi wesithombe ulingana nosayizi wento. Uma ukukhulisa isithombe kungu-< 1, usayizi wesithombe mncane kunosayizi wento.

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Isibalo selensi eqondile

Isibalo selensi ehlanganayo (eyi-convex) 1

s = do = ibanga lento, s' = di = ibanga lesithombe, ho = P P' = ukuphakama kwento, hi = Q Q' = ukuphakama kwesithombe, F1 noF2 = indawo ebalulekile yelensi ehlanganayo.

Unxantathu we-P'AP ufana nonxantathu we-Q'AQ. Ngakho-ke:

Isibalo selensi ehlanganayo (eyi-convex) 2

Unxantathu BF2A = Q'F2Q lapho ibanga lika-AB = ukuphakama kwento (h) kanye nebanga lika-F2A = ubude obuqondile (f) belensi eqondile. Ngakho-ke:

Isibalo selensi ehlanganayo (eyi-convex) 3

Isibalo selensi ehlanganayo (eyi-convex) 4

do = ibanga lento (elihle uma into idlula ngokukhanya)

di = ibanga lesithombe (elihle uma isithombe sidlula ngokukhanya noma isithombe singokoqobo)

f = ubude bokugxila (obuhle uma indawo yokugxila yelensi eqondile idlula ngokukhanya)

Khumbula njalo imithetho yezimpawu zamalensi aqondile uma usebenzisa lesi sibalo ukuxazulula inkinga yamalensi aqondile.

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Ukukhulisa isithombe (M)

Qaphela ukwakheka kwesithombe esingenhla. Njengonxantathu be-PAP 'ne-QAQ', singathola ubudlelwano phakathi kwebanga lento kanye nebanga lesithombe nokuphakama kwento kanye nokuphakama kwesithombe:

Isibalo selensi ehlanganayo (eyi-convex) 5

Isibalo esingenhla singabhalwa futhi njengoba singezansi ngokungeza uphawu u-m:

Isibalo selensi ehlanganayo (eyi-convex) 6

m = ukukhuliswa kwesithombe

ho = ukuphakama kwento (kuhle uma into ingaphezu kwe-axis eyinhloko yelensi eqondile noma into iqonde phezulu)

hi = ukuphakama kwesithombe (okungekuhle uma isithombe singaphansi kwe-axis eyinhloko yelensi eqondile noma isithombe siphendukezelwe)

do = ibanga lento (elihle uma into idlula ngokukhanya)

di = ibanga lesithombe (elihle uma isithombe sidluliswa ngokukhanya noma isithombe singokoqobo)