# Alternative method for solving this Calculus problem

#### Makanyaga

##### JF-Expert Member
ALTERNATIVE METHOD FOR SOLVING THIS CALCULUS PROBLEM

Dears calculators (by the way, what do you call the people who calculate?)

The method used in solving this calculus problem is superb but somehow the most difficult one!

Source: Geometric Applications of Line Integrals - Page 2

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#### Makanyaga

##### JF-Expert Member
Hivi hizi thread za namna hii hata ukiziweka kwenye Jukwaa la Elimu huwa hazipati wachangiaji?

#### mkorea

##### JF-Expert Member
Hilo swali umefanya wewe?

#### Makanyaga

##### JF-Expert Member
Hilo swali umefanya wewe?
La kwenye attachment nimefanya mimi. Swali halisi liko hapa
Source: Geometric Applications of Line Integrals - Page 2

Actually ninaandika manual mbili. Moja ya Differential Calculus na nyingine ya Integral Calculus. Zitakuwa na maswali zaidi ya 200 kwa ujumla wake. Maswali karibia yotei nimechukua kutoka kwenye document hii hapa:

http://www.staff.ttu.ee/~lpallas/Math_an2_exercises.pdf

Haya yote hayana njia ila yana majibu tu. Kwa hiyo na-solve mwenyewe na kuyawekea solutions sahihi na kuna baadhi yake, japo machache sana, majibu yake yamekosewa

Machache sana pia nachukua kutoka math24 website, ila ninapoona njia yao haifai, na-solve kwa kutumia njia yangu

Kuna mengine tena kama 20 hivi ni integral calculus, yaliwahi kuwekwa humu Jamiiforums mwaka 2013. Nayo nimeyachukua pia na nikishakamilisha, manual zote hizi mbili nitaziweka Public humu jukwaani. Kama wewe ni mdau basi siku nikikwama sehemu naweza kukushirikisha.

Yale ya mwaka 2013 haya hapa na tayari yote yana solutions zake:

Nawaachia Homework wale wa mambo yetu yaleee back in days (still got it?).....!!!!!

Ubarikiwe na Bwana

#### peno hasegawa

##### JF-Expert Member
Hivi hizi thread za namna hii hata ukiziweka kwenye Jukwaa la Elimu huwa hazipati wachangiaji?
Katiba inasema ujue kusoma na kuandika. Hamis Tambasamu wa Jimbo la sengerema na Joseph musukuma wa Geita vijijini unawafahamu? Hii mahesabu walikutana nayo wapi?

#### Makanyaga

##### JF-Expert Member
Katiba inasema ujue kusoma na kuandika. Hamis Tambasamu wa Jimbo la sengerema na Joseph musukuma wa Geita vijijini unawafahamu? Hii mahesabu walikutana nayo wapi?
Umesema wako Geita na Sengerema? Watakuwa walikutana nayo huko huko waliko. Kawaida kama unakutana na kitu, si ni lazima ukutane nacho pale pale ulipo, au?

#### Analyse

##### JF-Expert Member
La kwenye attachment nimefanya mimi. Swali halisi liko hapa
Source: Geometric Applications of Line Integrals - Page 2

Actually ninaandika manual mbili. Moja ya Differential Calculus na nyingine ya Integral Calculus. Zitakuwa na maswali zaidi ya 200 kwa ujumla wake. Maswali karibia yotei nimechukua kutoka kwenye document hii hapa:

http://www.staff.ttu.ee/~lpallas/Math_an2_exercises.pdf

Haya yote hayana njia ila yana majibu tu. Kwa hiyo na-solve mwenyewe na kuyawekea solutions sahihi na kuna baadhi yake, japo machache sana, majibu yake yamekosewa

Machache sana pia nachukua kutoka math24 website, ila ninapoona njia yao haifai, na-solve kwa kutumia njia yangu

Kuna mengine tena kama 20 hivi ni integral calculus, yaliwahi kuwekwa humu Jamiiforums mwaka 2012. Nayo nimeyachukua pia na nikishakamilisha, manual zote hizi mbili nitaziweka Public humu jukwaani. Kama wewe ni mdau basi siku nikikwama sehemu naweza kukushirikisha.
Ubarikiwe na Bwana
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.

#### Makanyaga

##### JF-Expert Member
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.
Wamepata majibu sahihi, waka-type vibaya, yaani ni typing error nadhani kwa sababu wao wameweka majibu tu. Naweza kukuonyesha mojawapo ya swali kama ukitaka
Hata hivyo, naomba pia nikuhakikishie kuwa nina uwezo wa kuwasahihisha wakikosea, uwezo huo ninao

#### Makanyaga

##### JF-Expert Member
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.
Kumbuka pia kuwa document yao ina majibu, haina njia

#### Analyse

##### JF-Expert Member
Kumbuka pia kuwa document yao ina majibu, haina njia
Ingekuwa na njia ndio ungeweza kuona, pengine kuna sehem umeteleza na ww.

#### Makanyaga

##### JF-Expert Member
Ingekuwa na njia ndio ungeweza kuona, pengine kuna sehem umeteleza na ww.
Hapana nina uhakika na ninachokisema. Kuna baadhi ya maswali, watakuwa wamekosea kuchapa majibu. Yaani wamesolve wakapta jibu sahihi, halafu mchapaji badala ya kuandika 34 akaandika 43, upo hapo? Tuseme ukifanya swali hata ukalirudia mata 3 au 4, unapata jibu lile lile tuseme la 34 lakini ukiangalia kwenye majibu yao unakuta wameandika jibu ni 43, hapo utasemaje?

#### Analyse

##### JF-Expert Member
Hapana nina uhakika na ninachokisema. Kuna baadhi ya maswali, wakosea kuchapa jibu. Yaani wamesolve wakapta jibu sahihi, halafu mchapaji badala ya kuandika 34 akaandika 43, upo hapo? Tuseme ukifanya swali hata ukalirudia mata 3 au 4, unapata jibu lile lile tuseme la 34 lakini ukiangalia kwenye majibu yao unakuta wameandika jibu ni 43, hapo utasemaje?
Watu kama ww ndio mlikuwa mnatupanikisha sisi wengine kwenye vyumba vya mitihani. Tunasolve na kupata jibu, alaf nyie mnawaambia maticha kuwa swali limekosea halifanyiki

#### Makanyaga

##### JF-Expert Member
Watu kama ww ndio mlikuwa mnatupanikisha sisi wengine kwenye vyumba vya mitihani. Tunasolve na kupata jibu, alaf nyie mnawaambia maticha kuwa swali limekosea halifanyiki
Sikuyasoma mimi haya shuleni, nimefundishwa ukubwani nikiwa tayari kazini, on-the-job training. Ukifundishwa ukiwa kazini tayari unakuwa na nafasi nzuri sana ya kuelewa zaidi kwa sababu kwanza akili inayotumika inakuwa ni ile ya ukubwani, na pili halafu hakuna mtihani. Nayaelewa kwa sababu nimefundishwa nikiwa kazini na nilikuwa sihitaji kufanya mitihani

#### Makanyaga

##### JF-Expert Member
More is to come in the near future, probably before the end of this year. You stay tuned

##### JF-Expert Member
La kwenye attachment nimefanya mimi. Swali halisi liko hapa
Source: Geometric Applications of Line Integrals - Page 2

Actually ninaandika manual mbili. Moja ya Differential Calculus na nyingine ya Integral Calculus. Zitakuwa na maswali zaidi ya 200 kwa ujumla wake. Maswali karibia yotei nimechukua kutoka kwenye document hii hapa:

http://www.staff.ttu.ee/~lpallas/Math_an2_exercises.pdf

Haya yote hayana njia ila yana majibu tu. Kwa hiyo na-solve mwenyewe na kuyawekea solutions sahihi na kuna baadhi yake, japo machache sana, majibu yake yamekosewa

Machache sana pia nachukua kutoka math24 website, ila ninapoona njia yao haifai, na-solve kwa kutumia njia yangu

Kuna mengine tena kama 20 hivi ni integral calculus, yaliwahi kuwekwa humu Jamiiforums mwaka 2013. Nayo nimeyachukua pia na nikishakamilisha, manual zote hizi mbili nitaziweka Public humu jukwaani. Kama wewe ni mdau basi siku nikikwama sehemu naweza kukushirikisha.

Yale ya mwaka 2013 haya hapa na tayari yote yana solutions zake:

Nawaachia Homework wale wa mambo yetu yaleee back in days (still got it?).....!!!!!

Ubarikiwe na Bwana
Hongera! Endelea mkuu, huu si tu ni msaada kwa wadau bali ni changamoto nzuri kwa wanaohitaji kunoa uwezo wao wa makihesabu.

Vile vile unafungua dirisha jipya la majadiliano na kuifanya JF kuwa na hadhi ya juu.

#### Makanyaga

##### JF-Expert Member
Hongera! Endelea mkuu, huu si tu ni msaada kwa wadau bali ni changamoto nzuri kwa wanaohitaji kunoa uwezo wao wa makihesabu.

Vile vile unafungua dirisha jipya la majadiliano na kuifanya JF kuwa na hadhi ya juu.
Naomba nikukumbushe tu kuwa JF iko juu sana tangu kipindi kirefu nyuma. Ubarikiwe pia kwa ushauri mzuri

#### Teknologist

##### JF-Expert Member
La kwenye attachment nimefanya mimi. Swali halisi liko hapa
Source: Geometric Applications of Line Integrals - Page 2

Actually ninaandika manual mbili. Moja ya Differential Calculus na nyingine ya Integral Calculus. Zitakuwa na maswali zaidi ya 200 kwa ujumla wake. Maswali karibia yotei nimechukua kutoka kwenye document hii hapa:

http://www.staff.ttu.ee/~lpallas/Math_an2_exercises.pdf

Haya yote hayana njia ila yana majibu tu. Kwa hiyo na-solve mwenyewe na kuyawekea solutions sahihi na kuna baadhi yake, japo machache sana, majibu yake yamekosewa

Machache sana pia nachukua kutoka math24 website, ila ninapoona njia yao haifai, na-solve kwa kutumia njia yangu

Kuna mengine tena kama 20 hivi ni integral calculus, yaliwahi kuwekwa humu Jamiiforums mwaka 2013. Nayo nimeyachukua pia na nikishakamilisha, manual zote hizi mbili nitaziweka Public humu jukwaani. Kama wewe ni mdau basi siku nikikwama sehemu naweza kukushirikisha.

Yale ya mwaka 2013 haya hapa na tayari yote yana solutions zake:

Nawaachia Homework wale wa mambo yetu yaleee back in days (still got it?).....!!!!!

Ubarikiwe na Bwana

Duuh!
We ni noma babu yake, Nimekubali
Sasa leta application zake kwenye real life, zitaleta mvuto
kuweka mamilinganyo mingi ya x na y , yanachosha kuangali mlolongo mrefu

Watu watapata mvuto kama utaweka Differential na Intregral Calculus application kwenye uchumi kama kutabiri viwango vya riba , takwimu hasa kwenye ongezeko la population ,kutabiri faida kwenye biashara

By the way , unasema umejifunza ukubwani ukiwa kazini, by interest ni kazi gani unafanya mpaka haya ni muhimu , teaching?
hata mimi mengi nimejituma baada ya kumaliza shule,

.

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