Alternative method for solving this Calculus problem

Makanyaga

JF-Expert Member
Sep 28, 2007
6,240
2,000
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)

Source: Geometric Applications of Line Integrals - Page 2
 

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Makanyaga

JF-Expert Member
Sep 28, 2007
6,240
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Hivi hizi thread za namna hii hata ukiziweka kwenye Jukwaa la Elimu huwa hazipati wachangiaji?
 

Makanyaga

JF-Expert Member
Sep 28, 2007
6,240
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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
Feb 24, 2016
2,188
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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
Sep 28, 2007
6,240
2,000
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
Jan 19, 2014
7,971
2,000
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
Sep 28, 2007
6,240
2,000
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
Sep 28, 2007
6,240
2,000
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
Jan 19, 2014
7,971
2,000
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
Sep 28, 2007
6,240
2,000
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
 

Zawadi Ngoda

JF-Expert Member
Aug 13, 2009
2,987
2,000
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.
 

Teknologist

JF-Expert Member
Oct 20, 2018
675
1,000
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,
 

Kijana matata

JF-Expert Member
Jul 21, 2017
558
500
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