Menene iyakar aiki

A cikin wannan ɗaba'ar, za mu yi la'akari da ɗaya daga cikin mahimman ra'ayoyin nazarin ilimin lissafi - iyakar aikin: ma'anarsa, da kuma mafita daban-daban tare da misalai masu amfani.

Ƙayyade iyakar aiki

Iyakar aiki - darajar da darajar wannan aikin ta dogara lokacin da hujjarsa ta kasance mai iyakancewa.

Iyakance rikodin:

• Ana nuna iyaka ta gunkin Lim;
• a ƙasa an ƙara abin da ƙimar hujja (mai canzawa) na aikin ke da'awar. Yawancin lokaci wannan x, amma ba lallai ba ne, misali:x→1″;
• sai a kara aikin da kansa a hannun dama, misali:

  

Don haka, rikodin ƙarshe na iyaka yayi kama da haka (a cikin yanayinmu):

Karatu kamar "iyakar aikin kamar yadda x ke kula da haɗin kai".

x→ 1 - wannan yana nufin cewa "x" yana ɗaukar ƙima da ƙima waɗanda ke kusanci haɗin kai mara iyaka, amma ba za su taɓa haɗuwa da shi ba (ba za a kai su ba).

Iyakar yanke shawara

Tare da lambar da aka bayar

Bari mu warware a sama iyaka. Don yin wannan, kawai canza naúrar a cikin aikin (saboda x→1):

Don haka, don warware iyakar, da farko muna ƙoƙarin musanya lambar da aka bayar a cikin aikin da ke ƙasa (idan x yana kula da takamaiman lamba).

Tare da rashin iyaka

A wannan yanayin, hujjar aikin yana ƙaruwa ba tare da iyaka ba, wato. "X" yana son rashin iyaka (∞). Misali:

If x→∞, sannan aikin da aka bayar ya kasance yana rage rashin iyaka (-∞), saboda:

• 3 - 1 = 2
• 3-10 = -7
• 3-100 = -97
• 3 - 1000 - 997 da dai sauransu.

Wani misali mafi rikitarwa

Domin warware wannan iyaka, kuma, kawai ƙara dabi'u x kuma dubi "halayen" na aikin a cikin wannan yanayin.

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

Don haka, don "X"kula da rashin iyaka, aikin x² 3x-6 ku girma har abada.

Tare da rashin tabbas (x yana kula da rashin iyaka)

A wannan yanayin, muna magana ne game da iyakoki, lokacin da aikin ya zama juzu'i, mai ƙididdigewa da ƙididdigewa wanda shine polynomials. Inda "X" yana kula da rashin iyaka.

Example: bari mu lissafta iyaka a kasa.

Magani

Kalmomin da ke cikin duka mai ƙididdigewa da maƙasudi sun kasance marasa iyaka. Ana iya ɗauka cewa a cikin wannan yanayin maganin zai kasance kamar haka:

Duk da haka, ba duka ba ne mai sauƙi. Don warware iyakar muna buƙatar yin haka:

1. Nemo x zuwa mafi girman iko ga mai ƙididdigewa (a cikin yanayinmu, biyu ne).

2. Hakazalika, mun ayyana x zuwa mafi girman iko ga ƙididdiga (kuma yana daidai da biyu).

3. Yanzu mun raba biyu da ƙididdiga da ƙididdiga ta x a babban digiri. A cikin yanayinmu, a cikin lokuta biyu - a cikin na biyu, amma idan sun bambanta, ya kamata mu dauki matsayi mafi girma.

4. A sakamakon sakamakon, duk ɓangarorin suna da alaƙa da sifili, don haka amsar ita ce 1/2.

Tare da rashin tabbas (x yana kula da takamaiman lamba)

Duka mai ƙididdigewa da mai ƙididdigewa suna da yawa, duk da haka, "X" yana kula da takamaiman lamba, ba ga rashin iyaka ba.

A wannan yanayin, muna rufe idanunmu bisa sharadi ga gaskiyar cewa ma'aunin sifili ne.

Example: Bari mu nemo iyakar aikin da ke ƙasa.

Magani

1. Da farko, bari mu musanya lamba 1 a cikin aikin, wanda "X". Mun sami rashin tabbas na fom da muke la'akari.

2. Na gaba, za mu lalata ƙididdiga da ƙididdiga zuwa dalilai. Don yin wannan, zaka iya amfani da ƙayyadaddun ƙididdiga masu yawa, idan sun dace, ko.

A wajenmu, tushen magana a cikin ƙididdiga (2x² - 5x + 3 = 0) su ne lambobi 1 da 1,5. Don haka, ana iya wakilta shi kamar: 2 (x-1) (x-1,5).

Ƙididdigar (x-1) da farko mai sauƙi ne.

3. Muna samun irin wannan iyakacin da aka gyara:

4. Ana iya rage juzu'in ta (x-1):

5. Ya rage kawai don musanya lamba 1 a cikin magana da aka samu a ƙarƙashin iyaka: