Mienzaniso yeMibvunzo Inotaura Nezvekuwanza uye Kugovaniswa kweMabasa
Mumasvomhu, basa ihukama hunobatanidza chinhu chimwe nechimwe cheseti imwe nechinhu chimwe chete mune imwe seti. Basa rinowanzo kutaurwa se \( f(x) \), zvichireva kuti \( f \) ibasa re \( x \). Rimwe remabasa anogona kuitwa nemabasa kuwanda nekuparadzanisa. Muchinyorwa chino, tichaongorora matambudziko akati wandei emuenzaniso uye tichakurukura mashandiro ekuwanda nekuparadzanisa emabasa.
Kuwanda Kwemabasa
Kuwanda kwebasa (function multiplication) inzira yekuti tiwedzere mabasa maviri uye mhedzisiro yacho ibasa idzva. Ngatitii tine mabasa maviri \( f(x) \) uye \( g(x) \). Chibereko chemabasa maviri aya chinogona kutaurwa se \( (f \cdot g)(x) \) kana \( f(x) \cdot g(x) \).
Muenzaniso Mubvunzo 1:
Zvichipiwa mabasa maviri:
– \( f(x) = 2x + 3 \)
– \( g(x) = x^2 – 4 \)
Tsvaga mhedzisiro ye \( f(x) \cdot g(x) \).
Kukurukurirana:
Chibereko chemabasa maviri aya ndeichi:
\[ (f \cdot g)(x) = f(x) \cdot g(x) \]
Kuti:
\[ (f \cdot g)(x) = (2x + 3) \cdot (x^2 – 4) \]
Kuti tiwedzere mapolynomial maviri, tinoshandisa distributive:
\[ (2x + 3)(x^2 – 4) = 2x(x^2) + 2x(-4) + 3(x^2) + 3(-4) \]
\[ = 2x^3 – 8x + 3x^2 – 12 \]
Saka mhedzisiro yekupedzisira ndeiyi:
\[ (f \cdot g)(x) = 2x^3 + 3x^2 – 8x – 12 \]
Muenzaniso Mubvunzo 2:
Basa rakapihwa:
– \( f(x) = \chivi(x) \)
– \( g(x) = \cos(x) \)
Tsvaga mhedzisiro ye \( f(x) \cdot g(x) \).
Kukurukurirana:
Chibereko chemabasa maviri aya ndeichi:
\[ (f \cdot g)(x) = \sin(x) \cdot \cos(x) \]
Saka mhedzisiro yekupedzisira ndeiyi:
\[ (f \cdot g)(x) = \sin(x) \cos(x) \]
Mu trigonometry, tinoziva kuti:
\[ \chivi(x) \cos(x) = \frac{1}{2} (\chivi(2x)) \]
Saka, mhedzisiro yekuwedzera mabasa aya ndeiyi:
\[ (f \cdot g)(x) = \frac{1}{2} \sin(2x) \]
Chikamu cheMabasa
Kupatsanurana kwebasa (function division) zvinoreva kupatsanura rimwe basa nerimwe wowana basa idzva, chero bedzi divisor isina kuenzana ne zero. Ngatitii tine mabasa maviri \( f(x) \) uye \( g(x) \). Kupatsanurana kwebasa iri kunogona kutaurwa se \( \left( \frac{f}{g} \right(x) \) kana \( \frac{f(x)}{g(x)} \).
Muenzaniso Mubvunzo 3:
Zvichipiwa mabasa maviri:
– \( f(x) = x^2 – 1 \)
– \( g(x) = x – 1 \)
Tsvaga mhedzisiro ye \( \frac{f(x)}{g(x)} \).
Kukurukurirana:
Kupatsanurwa kwemabasa maviri aya ndekwekuti:
\[ \left( \frac{f}{g} \right(x) = \frac{f(x)}{g(x)} \]
Kuti:
\[ \left( \frac{f}{g} \right(x) = \frac{x^2 – 1}{x – 1} \]
Tinogona kurerutsa zvikamu nekutarisa nhamba:
\[ x^2 – 1 = (x + 1)(x – 1) \]
Saka:
\[ \left( \frac{f}{g} \right(x) = \frac{(x + 1)(x – 1)}{x – 1} \]
Zvichienderana nekuti \( x \neq 1 \), tinogona kukanzura \( (x - 1) \) munhamba nedhinominator:
\[ \left( \frac{f}{g} \right(x) = x + 1 \]
Muenzaniso Mubvunzo 4:
Zvichipiwa mabasa maviri:
– \( f(x) = e^x \)
– \( g(x) = x \)
Tsvaga mhedzisiro ye \( \frac{f(x)}{g(x)} \).
Kukurukurirana:
Kupatsanurwa kwemabasa maviri aya ndekwekuti:
\[ \left( \frac{f}{g} \right(x) = \frac{e^x}{x} \]
Saka mhedzisiro yekupedzisira ndeiyi:
\[ \left( \frac{f}{g} \right(x) = \frac{e^x}{x} \]
Muenzaniso Mubvunzo 5:
Basa rakapihwa:
– \( f(x) = \ln(x) \)
– \( g(x) = x^2 \)
Tsvaga mhedzisiro ye \( \frac{f(x)}{g(x)} \).
Kukurukurirana:
Kupatsanurwa kwemabasa maviri aya ndekwekuti:
\[ \left( \frac{f}{g} \right(x) = \frac{\ln(x)}{x^2} \]
Saka mhedzisiro yekupedzisira ndeiyi:
\[ \left( \frac{f}{g} \right(x) = \frac{\ln(x)}{x^2} \]
Mhedziso
Kuwanda nekupatsanura mabasa ipfungwa huru mumasvomhu uye zvinobatsira zvikuru mukushandiswa kwakasiyana-siyana, mumasvomhu chaiwo uye mune zvesainzi zvinoshandiswa zvakaita sefizikisi neinjiniya. Nekunzwisisa maitiro ekuwanda nekupatsanura mabasa, tinogona kugadzirisa matambudziko akasiyana-siyana anosanganisira iwo. Kukurukurirana kwematambudziko ari pamusoro apa kunopa nzwisiso yekuti tingaita sei mabasa aya uye mhedzisiro yakawanikwa.
Ramba uchidzidzira kuti unzwisise zvakadzama zvinhu izvi, sezvo kunzwisisa kwakasimba kwemabasa ekushanda kwakakosha pakufambira mberi muzvidzidzo zvemasvomhu. Kana ukasangana nematambudziko, usazeza kubvunza mudzidzisi wako kana kutsvaga zvimwe zvekushandisa pakudzidza. Tinovimba kuti chinyorwa chino chave chichibatsira mukunzwisisa kuwanda nekupatsanura mabasa.
