Mienzaniso yeMibvunzo Inotaura Nezvekuwedzera nekubvisa Mabasa
Kuwedzerwa nekubvisa mabasa ipfungwa huru uye yakakosha mumasvomhu. Pfungwa iyi haingokoshi chete muzvidzidzo asiwo ine mashandisirwo akawanda anoshanda muhupenyu hwezuva nezuva nedzimwe nzvimbo dzekudzidza. Muchinyorwa chino, tichakurukura mienzaniso yakati wandei yematambudziko ekuwedzera nekubvisa, pamwe chete netsananguro dzakadzama.
Tsanangudzo Dzekutanga uye Pfungwa
Tisati tapinda mumibvunzo yemuenzaniso, ngatikurukurei zvishoma nezve tsananguro uye pfungwa huru dzemabasa ekuwedzera nekubvisa.
Kuwedzera Basa
Kana tiine mabasa maviri \( f(x) \) uye \( g(x) \), saka huwandu hwemabasa maviri aya ibasa idzva rinotsanangurwa se:
\[ (f + g)(x) = f(x) + g(x) \]
Kuderedza Basa
Kubvisa mabasa kunotsanangurwawo nenzira yakafanana nekuwedzera mabasa. Kana tiine mabasa maviri \( f(x) \) uye \( g(x) \), saka kubvisa mabasa maviri aya ibasa idzva rinotsanangurwa se:
\[ (f – g)(x) = f(x) – g(x) \]
Mibvunzo yemuenzaniso nekukurukurirana
Ngatitarisei mimwe mienzaniso yezvinetso kuti tijekese pfungwa iyi.
Muenzaniso 1: Kuwedzera kweMabasa Akatsetseka
Ngatitii \( f(x) = 2x + 3 \) uye \( g(x) = x – 1 \). Sarudza \( (f + g)(x) \).
Kukurukurirana:
Tinogona kuwedzera mabasa maviri aya nekuwedzera mazwi anoenderana.
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = (2x + 3) + (x – 1)
\]
\[
(f + g)(x) = 2x + x + 3 – 1
\]
\[
(f + g)(x) = 3x + 2
\]
Saka, \( (f + g)(x) = 3x + 2 \).
Muenzaniso 2: Kubvisa Mabasa Akatsetseka
Ngatitii \( f(x) = 4x + 5 \) uye \( g(x) = 2x – 3 \). Sarudza \( (f – g)(x) \).
Kukurukurirana:
Tinogona kuderedza mabasa ese ari maviri nekubvisa mazwi anoenderana.
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = (4x + 5) – (2x – 3)
\]
\[
(f – g)(x) = 4x + 5 – 2x + 3
\]
\[
(f – g)(x) = 2x + 8
\]
Saka, \( (f – g)(x) = 2x + 8 \).
Muenzaniso 3: Kuwedzera kweMashandiro eQuadratic
Ngatitii \( f(x) = x^2 + 2x + 1 \) uye \( g(x) = -x^2 + 4x – 3 \). Sarudza \( (f + g)(x) \).
Kukurukurirana:
Tinogona kuwedzera mabasa maviri aya nekuwedzera mazwi anoenderana.
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = (x^2 + 2x + 1) + (-x^2 + 4x – 3)
\]
\[
(f + g)(x) = x^2 – x^2 + 2x + 4x + 1 – 3
\]
\[
(f + g)(x) = 6x – 2
\]
Saka, \( (f + g)(x) = 6x – 2 \).
Muenzaniso 4: Kubvisa Mabasa eQuadratic
Ngatitii \( f(x) = 3x^2 – 2x + 4 \) uye \( g(x) = x^2 + x – 5 \). Sarudza \( (f – g)(x) \).
Kukurukurirana:
Tinogona kuderedza mabasa ese ari maviri nekubvisa mazwi anoenderana.
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = (3x^2 – 2x + 4) – (x^2 + x – 5)
\]
\[
(f – g)(x) = 3x^2 – x^2 – 2x – x + 4 + 5
\]
\[
(f – g)(x) = 2x^2 – 3x + 9
\]
Saka, \( (f – g)(x) = 2x^2 – 3x + 9 \).
Muenzaniso 5: Kuwedzera nekubvisa mabasa eExponential
Ngatitii \( f(x) = e^x \) uye \( g(x) = e^{-x} \). Sarudza:
1. \( (f + g)(x) \)
2. \( (f – g)(x) \)
Kukurukurirana:
1. Basa rekuwedzera:
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = e^x + e^{-x}
\]
Saka, \( (f + g)(x) = e^x + e^{-x} \).
2. Kuderedza Basa:
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = e^x – e^{-x}
\]
Saka, \( (f – g)(x) = e^x – e^{-x} \).
Muenzaniso 6: Kuwedzera nekubvisa mabasa eTrigonometric
Ngatitii \( f(x) = \sin x \) uye \( g(x) = \cos x \). Sarudza:
1. \( (f + g)(x) \)
2. \( (f – g)(x) \)
Kukurukurirana:
1. Basa rekuwedzera:
\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = \chivi x + \cos x
\]
Saka, \( (f + g)(x) = \sin x + \cos x \).
2. Kuderedza Basa:
\[
(f – g)(x) = f(x) – g(x)
\]
\[
(f – g)(x) = \chivi x – \cos x
\]
Saka, \( (f – g)(x) = \sin x – \cos x \).
Muenzaniso 7: Kushandiswa kweKuwedzera neKubvisa Mabasa muMatambudziko eMuviri
Ngatitii pane mabasa maviri anotsanangura nzvimbo (mumamita) yemotokari mbiri dziri kufamba munzira imwe chete munguva \(t \) (mumasekonzi).
Mota A: \( f(t) = 5t + 2 \)
Mota B: \( g(t) = 3t + 4 \)
Sarudza:
1. Nzvimbo yakabatana yemotokari mbiri idzi.
2. Musiyano uripo pakati pemotokari mbiri panguva imwe chete.
Kukurukurirana:
1. Basa rekuwedzera:
\[
(f + g)(t) = f(t) + g(t)
\]
\[
(f + g)(t) = (5t + 2) + (3t + 4)
\]
\[
(f + g)(t) = 8t + 6
\]
Saka, nzvimbo yakabatana yemotokari mbiri panguva \(t \) ndeye \(8t + 6 \) mamita.
2. Kuderedza Basa:
\[
(f – g)(t) = f(t) – g(t)
\]
\[
(f – g)(t) = (5t + 2) – (3t + 4)
\]
\[
(f – g)(t) = 2t – 2
\]
Saka, musiyano uripo pakati pemotokari mbiri panguva imwe chete ndiwo mamita maviri (2t – 2) (2t – 2).
Mhedziso
Kuwedzera nekubvisa mabasa ipfungwa dzakakosha zvikuru mumasvomhu. Tinogona kuwedzera kana kubvisa mabasa maviri nekuwedzera kana kubvisa mazwi anoenderana nawo. Pfungwa iyi haingobatsiri chete muzvidzidzo, asiwo ine mashandisirwo akawanda anoshanda. Kuburikidza nemibvunzo yakasiyana-siyana iri pamusoro, tinotarisira kuti vaverengi vanzwisise pfungwa iyi zviri nani.
