He aha ka palena o kahi hana

Ma kēia hoʻolaha, e noʻonoʻo mākou i kekahi o nā manaʻo nui o ka nānā ʻana i ka makemakika - ka palena o kahi hana: kona wehewehe ʻana, a me nā hoʻonā like ʻole me nā hiʻohiʻona kūpono.

Hoʻoholo i ka palena o kahi hana

palena hana – ka waiwai e pili ana ka waiwai o keia hana ke huli kona manao i ka palena palena.

Ka palena mooolelo:

• hōʻike ʻia ka palena e ka ikona lime;
• ma lalo iho ua hoʻohui ʻia ka waiwai o ka hoʻopaʻapaʻa (variable) o ka hana. ʻO ka mea maʻamau kēia x, akā ʻaʻole pono, no ka laʻana:x→1″;
• a laila hoʻohui ʻia ka hana ponoʻī ma ka ʻākau, no ka laʻana:

  

No laila, ʻo ka moʻolelo hope o ka palena e like me kēia (i kā mākou hihia):

Heluhelu like "ka palena o ka hana e like me ka manaʻo o x i ka lokahi".

x→ 1 - ʻo ia ke ʻano o ka "x" e lawe mau i nā waiwai e pili kokoke ana i ka lokahi, akā ʻaʻole loa e hui pū me ia (ʻaʻole e loaʻa).

Nā palena hoʻoholo

Me ka helu helu

E hoʻoholo kākou i ka palena ma luna. No ka hana ʻana i kēia, e hoʻololi wale i ka ʻāpana i ka hana (no ka mea x→1):

No laila, e hoʻoholo i ka palena, e hoʻāʻo mua mākou e hoʻololi i ka helu i hāʻawi ʻia i loko o ka hana ma lalo o ia (inā makemake ʻo x i kahi helu kikoʻī).

Me ka pau ole

I kēia hihia, piʻi ʻole ka hoʻopaʻapaʻa o ka hana, ʻo ia hoʻi, "X" hele i ka palena ʻole (∞). ʻo kahi laʻana:

If x→∞, a laila hoʻemi ka hana i hāʻawi ʻia i ka palena ʻole (-∞), no ka mea:

• 3 - 1 = 2
• 3 – 10 = -7
• 3 – 100 = -97
• 3 – 1000 – 997 etc.

ʻO kekahi laʻana paʻakikī ʻē aʻe

I mea e hoʻoponopono ai i kēia palena, e hoʻonui wale i nā waiwai x a nānā i ka "hana" o ka hana ma kēia hihia.

• RџSЂRё x = 1, y = 1² + 3 · 1 – 6 = -2
• RџSЂRё x = 10, y = 10² + 3 · 10 – 6 = 124
• RџSЂRё x = 100, y = 100² + 3 · 100 – 6 = 10294

Pēlā, no ka mea "X"ka manaʻo i ka pau ʻole, ka hana x² + 3x - 6 ulu mau loa.

Me ka maopopo ʻole (x ke alo i ka palena ʻole)

I kēia hihia, ke kamaʻilio nei mākou e pili ana i nā palena, inā he hapa ka hana, ʻo ka helu a me ka denominator he polynomial. Ma kahi "X" hele i ka palena ʻole.

la'ana: e helu kakou i ka palena malalo.

pāʻoihana

ʻO nā ʻōlelo ma ka helu helu a me ka denominator e pili ana i ka palena ʻole. Hiki ke manaʻo ʻia ma kēia ʻano ka hopena e like me kēia:

Akā naʻe, ʻaʻole maʻalahi nā mea a pau. No ka hoʻoholo i ka palena, pono mākou e hana i kēia:

1. E ʻike x i ka mana kiʻekiʻe loa no ka helu (ma kā mākou hihia, ʻelua).

2. Pēlā nō, wehewehe mākou x i ka mana kiʻekiʻe loa no ka denominator (ua like pū me ʻelua).

3. Ano, puunaue kakou i ka huahelu a me ka denominator ma x ma ke kula kiʻekiʻe. I ko mākou hihia, i nā hihia ʻelua - i ka lua, akā inā ʻokoʻa lākou, pono mākou e lawe i ke kiʻekiʻe kiʻekiʻe.

4. I ka hopena o ka hopena, pili nā hakina a pau i ka ʻole, no laila ʻo 1/2 ka pane.

Me ka maopopo ʻole (ʻo x i kahi helu kikoʻī)

He mau polynomial ka helu a me ka denominator, akā naʻe, "X" he helu kikoʻī, ʻaʻole i ka palena ʻole.

I kēia hihia, pani mākou i ko mākou mau maka i ka ʻoiaʻiʻo ʻo ka denominator he zero.

la'ana: E ʻimi kākou i ka palena o ka hana ma lalo nei.

pāʻoihana

1. ʻO ka mua, e hoʻololi kākou i ka helu 1 i loko o ka hana, kahi "X". Loaʻa iā mākou ka maopopo ʻole o ke ʻano a mākou e noʻonoʻo nei.

2. A laila, hoʻokaʻawale mākou i ka helu a me ka helu i mau kumu. No ka hana ʻana i kēia, hiki iā ʻoe ke hoʻohana i nā hoʻohālikelike hoʻonui pōkole, inā kūpono lākou, a i ʻole.

I ko mākou hihia, nā aʻa o ka ʻōlelo ma ka helu helu (2x² – 5x + 3 = 0) ʻo ia nā helu 1 a me 1,5. No laila, hiki ke hōʻike ʻia e like me: 2(x-1)(x-1,5).

ka helu (x–1) he mea maʻalahi ma mua.

3. Loaʻa iā mākou kahi palena i hoʻololi ʻia:

4. Hiki ke hoemiia ka hakina e (x–1):

5. E hoʻololi wale i ka helu 1 ma ka ʻōlelo i loaʻa ma lalo o ka palena.