Alternative method for solving this Calculus problem

Makanyaga

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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!
Please enjoy your reading with this somehow simpler method of solving the same problem (please see the attachment below)

<iframe src="https://docs.google.com/document/d/...Y570MuGhcnRJUaD7xjoJJheTrCt/pub?embedded=true"></iframe>

Source: Geometric Applications of Line Integrals - Page 2
 

Attachments

Hivi hizi thread za namna hii hata ukiziweka kwenye Jukwaa la Elimu huwa hazipati wachangiaji?
 
mkorea said:
Hilo swali umefanya wewe?
Click to expand...
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
 
Makanyaga said:
Hivi hizi thread za namna hii hata ukiziweka kwenye Jukwaa la Elimu huwa hazipati wachangiaji?
Click to expand...
Katiba inasema ujue kusoma na kuandika. Hamis Tambasamu wa Jimbo la sengerema na Joseph musukuma wa Geita vijijini unawafahamu? Hii mahesabu walikutana nayo wapi?
 
peno hasegawa said:
Katiba inasema ujue kusoma na kuandika. Hamis Tambasamu wa Jimbo la sengerema na Joseph musukuma wa Geita vijijini unawafahamu? Hii mahesabu walikutana nayo wapi?
Click to expand...
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?
 
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.
 
Analyse said:
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.
Click to expand...
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
 
Analyse said:
Yani watu wamesolve huko na kupata majibu kisha wakatengenezea documents vizuri. Ww unakuja kusema majibu yamekosewa, kuwa serious broh.
Click to expand...
Kumbuka pia kuwa document yao ina majibu, haina njia
 
Analyse said:
Ingekuwa na njia ndio ungeweza kuona, pengine kuna sehem umeteleza na ww.
Click to expand...
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?
 
Watu kama ww ndio mlikuwa mnatupanikisha sisi wengine kwenye vyumba vya mitihani. Tunasolve na kupata jibu, alaf nyie mnawaambia maticha kuwa swali limekosea halifanyiki
 
Analyse said:
Watu kama ww ndio mlikuwa mnatupanikisha sisi wengine kwenye vyumba vya mitihani. Tunasolve na kupata jibu, alaf nyie mnawaambia maticha kuwa swali limekosea halifanyiki
Click to expand...
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
 
More is to come in the near future, probably before the end of this year. You stay tuned
 
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.
 
Zawadi Ngoda said:
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.
Click to expand...
Naomba nikukumbushe tu kuwa JF iko juu sana tangu kipindi kirefu nyuma. Ubarikiwe pia kwa ushauri mzuri
 

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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