Kev nrawm yog txhais raws li qhov nrawm ntawm cov khoom hauv qee qhov kev taw qhia. Hauv ntau qhov xwm txheej, txhawm rau nrhiav qhov nrawm, peb tuaj yeem siv qhov sib npaug v = s/t, qhov twg v sib npaug nrawm, s sib npaug tag nrho cov nrug uas cov khoom tau txav los ntawm nws txoj haujlwm pib, thiab t sib npaug sijhawm. Txawm li cas los xij, txoj hauv kev no tsuas yog muab tus nqi "nruab nrab" nrawm ntawm qhov khoom hla nws qhov kev txav chaw. Siv laij lej, koj tuaj yeem suav qhov nrawm ntawm ib qho khoom ntawm txhua qhov chaw raws nws qhov kev txav chaw. Tus nqi no hu ua "nrawm nrawm" thiab tuaj yeem suav los ntawm qhov kev ua zauv v = (ds)/(dt), lossis, ua lwm yam lus, yog qhov sib piv ntawm qhov sib npaug rau qhov nrawm nrawm ntawm qhov khoom.
Kauj ruam
Txoj Kev 1 ntawm 3: Xam Tawm Ceev
Kauj Ruam 1. Pib nrog qhov sib npaug rau qhov nrawm ntawm cov khoom txav mus los
Txhawm rau kom tau txais tus nqi ntawm kev nrawm nrawm ntawm cov khoom, peb yuav tsum xub muaj qhov sib npaug uas piav qhia nws txoj haujlwm (raws li nws qhov kev hloov chaw) ntawm qhov chaw nyob hauv lub sijhawm. Qhov no txhais tau tias qhov sib npaug yuav tsum muaj qhov sib txawv s (uas sawv ib leeg) ntawm ib sab, thiab t ntawm qhov tod tes (tab sis tsis tas yuav nyob ib leeg), zoo li no:
s = -1.5t2+10t+4
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Hauv qhov sib npaug, qhov sib txawv yog:
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Kev tshem tawm = s. Ntawd yog qhov kev mus los ntawm qhov khoom los ntawm nws qhov pib. Piv txwv li, yog tias ib yam khoom taug kev 10 metres rau pem hauv ntej thiab 7 meters rov qab, tom qab ntawd tag nrho cov kev mus ncig yog 10 - 7 = 3 meters (tsis yog 10 + 7 = 17 meters).
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Sijhawm = t. Qhov kev hloov pauv no yog piav qhia tus kheej. Feem ntau qhia hauv vib nas this. # Siv qhov sib piv ntawm qhov sib npaug. Cov txiaj ntsig ntawm qhov kev ua zauv yog lwm qhov kev ua zauv uas tuaj yeem muab tus nqi nqes hav los ntawm qee kis. Txhawm rau nrhiav qhov sib piv ntawm cov mis rau kev txav chaw ntawm ib yam khoom, muab lub luag haujlwm siv cov cai hauv qab no: Yog y = a*x , Derivative = a*n*xn-1 ib. Txoj cai no siv rau txhua feem uas nyob ntawm "t" sab ntawm kab zauv.
Xam Tam Sim No Tshaj Tawm Kauj Ruam 2
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- Hauv lwm lo lus, pib los ntawm nqis "t" sab ntawm qhov sib npaug ntawm sab laug mus rau sab xis. Txhua lub sijhawm koj mus txog tus "t" tus nqi, rho tawm 1 los ntawm tus lej nthuav tawm thiab sib npaug tag nrho los ntawm thawj qhov nthuav tawm. Ib qho tsis tu ncua (qhov sib txawv uas tsis muaj "t") yuav ploj mus vim tias lawv tau sib tw los ntawm 0. Cov txheej txheem no tsis nyuaj li ib tus neeg xav, cia peb muab qhov sib npaug hauv cov kauj ruam saum toj no ua piv txwv:
s = -1.5t2+10t+4
(2) -1.5t(2-1)+ (1) 10t1 - 1 + (0) 4t0
-3t ib1 + 10 hli0
- 3 Txa + 10
Kauj Ruam 2. Hloov qhov sib txawv "s" nrog "ds/dt
"Txhawm rau qhia tias koj qhov kev ua zauv tshiab yog qhov ua piv txwv ntawm qhov sib npaug yav dhau los, hloov" s "nrog" ds/dt ". /dt yog tus nqi ntawm txoj kab nqes (nqes hav) ntawm ib qho taw tes hauv thawj qhov kev ua zauv, piv txwv li, txhawm rau txiav txim siab txoj kab nqes ntawm kab uas tau kos los ntawm kab zauv s = -1.5t2 + 10t + 4 ntawm t = 5, peb tuaj yeem ntsaws tus nqi "5" rau hauv cov lej sib npaug.
- Hauv qhov piv txwv siv, thawj qhov ua piv txwv sib npaug tam sim no yuav zoo li no:
ds/sec = -3t + 10
Kauj Ruam 3. Plug tus nqi t mus rau qhov sib npaug tshiab kom tau txais tus nqi nrawm nrawm
Tam sim no koj muaj cov lej sib npaug, nws yooj yim los nrhiav qhov nrawm nrawm ntawm ib qho twg. Txhua yam koj yuav tsum tau ua yog xaiv tus nqi rau t thiab ntsaws nws rau hauv koj qhov kev sib npaug derivative. Piv txwv li, yog tias koj xav nrhiav qhov nrawm nrawm ntawm t = 5, koj tuaj yeem hloov tus nqi ntawm t nrog "5" hauv qhov sib npaug derivative ds/dt = -3 + 10. Tom qab ntawd daws cov kab zauv zoo li no:
ds/sec = -3t + 10
ds/sec = -3 (5) + 10
ds/sec = -15 + 10 = - 5 meters/thib ob
Nco tseg tias chav tsev siv saum toj no yog "meter/second". Vim tias qhov peb suav xam yog kev hloov chaw nyob rau hauv cov ntsuas thiab lub sijhawm hauv vib nas this (vib nas this) thiab qhov nrawm feem ntau yog kev hloov chaw nyob rau qee lub sijhawm, chav tsev no tsim nyog siv
Txoj Kev 2 ntawm 3: Txheeb Duab Txheeb Txog Kev Ceev Ceev
Kauj Ruam 1. Kos kab duab ntawm qhov khoom txav mus los lub sijhawm
Hauv ntu lus saum toj no, qhov sib piv tau hais los ua qauv rau kev nrhiav txoj kab nqes ntawm ib qho taw tes rau qhov sib npaug uas koj tau txais. Qhov tseeb, yog tias koj sawv cev rau qhov khoom txav mus raws kab ntawm kab ntawv, "txoj kab nqes ntawm kab ntawm txhua lub ntsiab lus yog sib npaug rau tus nqi ntawm nws qhov nrawm nrawm ntawm qhov ntawd."
- Txhawm rau piav qhia kev txav chaw ntawm ib yam khoom, siv x los sawv cev rau lub sijhawm thiab y los sawv cev rau kev hloov chaw. Tom qab ntawd kos cov ntsiab lus, ntsaws tus nqi t rau hauv koj qhov kev ua zauv, yog li tau txais tus nqi s rau koj daim duab, kos t, s hauv kab ntawv raws li (x, y).
- Nco ntsoov tias koj daim duab tuaj yeem nthuav dav hauv qab x-axis. Yog tias kab sawv cev rau kev txav ntawm koj lub hom phiaj mus txog qis dua x-axis, nws txhais tau tias cov khoom tau txav rov qab los ntawm nws thawj txoj haujlwm. Feem ntau, koj daim duab yuav tsis ncav lub nraub qaum ntawm y -axis - vim tias peb tsis ntsuas qhov nrawm ntawm cov khoom txav mus los!
Kauj Ruam 2. Xaiv ib qho uas nyob ib sab P thiab Q hauv kab
Txhawm rau kom tau txais txoj kab nqes ntawm kab ntawm P, peb tuaj yeem siv qhov dag uas hu ua "noj qhov txwv." Kev txwv qhov cuam tshuam nrog ob lub ntsiab lus (P thiab Q, ib qho chaw nyob ze) ntawm kab nkhaus thiab nrhiav txoj kab nqes ntawm txoj kab los ntawm kev txuas lawv ntau zaus kom txog thaum P thiab Q ze dua.
Cia peb hais cov khoom txoj kab kev txav chaw muaj qhov tseem ceeb (1, 3) thiab (4, 7). Hauv qhov no, yog tias peb xav nrhiav txoj kab nqes ntawm qhov chaw (1, 3), peb tuaj yeem txiav txim siab (1, 3) = P thiab (4, 7) = Q.
Kauj Ruam 3. Nrhiav txoj kab nqes nruab nrab ntawm P thiab Q
Txoj kab nqes nruab nrab ntawm P thiab Q yog qhov sib txawv hauv y qhov tseem ceeb rau P thiab Q raws x-axis tus nqi sib txawv rau P thiab Q. Hauv lwm lo lus, H = (yQ -ib yP)/(xwmQ -x ibP), qhov twg H yog txoj kab nqes nruab nrab ntawm ob lub ntsiab lus. Hauv peb qhov piv txwv, tus nqi ntawm txoj kab nqes ntawm P thiab Q yog
H = (yQ-ib yP)/(xwmQ-x ibP)
H = (7 - 3)/(4 - 1)
H = (4)/(3) = 1.33
Kauj Ruam 4. Rov ua dua ob peb zaug, txav Q ze rau P
Koj lub hom phiaj yog txhawm rau txo qhov kev ncua deb ntawm P thiab Q kom zoo ib yam li tus dot. Qhov ze ntawm qhov ze ntawm P thiab Q, ze dua txoj kab nqes ntawm kab P. Ua qhov no ntau zaus nrog cov kab zauv siv ua piv txwv, siv cov ntsiab lus (2, 4.8), (1.5, 3.95), thiab (1.25, 3.49) raws li Q thiab qhov pib (1, 3) raws li P:
Q = (2, 4.8):
H = (4.8 - 3)/(2 - 1)
H = (1.8)/(1) = 1.8
Q = (1.5, 3.95):
H = (3.95 - 3)/(1.5 - 1)
H = (.95)/(. 5) = 1.9
Q = (1.25, 3.49):
H = (3.49 - 3)/(1.25 - 1)
H = (.49)/(. 25) = 1.96
Kauj Ruam 5. Kwv yees txoj kab nqes ntawm kab kom deb me ntsis
Raws li Q tau los ze zog rau P, H tau los ze dua thiab ze rau tus nqi ntawm txoj kab nqes ntawm qhov taw tes P. Thaum kawg, thaum nws mus txog tus nqi me me, H sib npaug txoj kab nqes ntawm P. Txij li thaum peb tsis tuaj yeem ntsuas lossis suav nrug deb me me, peb tsuas tuaj yeem kwv yees txoj kab nqes ntawm P tom qab nws pom tseeb los ntawm qhov peb tab tom sim.
- Hauv qhov piv txwv, thaum peb txav Q ze rau P, peb tau txais qhov tseem ceeb ntawm 1.8, 1.9, thiab 1.96 rau H.
- Nco ntsoov tias txoj kab nqes ntawm ib qho taw tes ntawm kab yog sib npaug ntawm qhov sib npaug ntawm kab. Txij li cov kab siv qhia pom kev txav chaw ntawm cov khoom nyob rau lub sijhawm, thiab vim tias peb tau pom hauv ntu yav dhau los, qhov nrawm nrawm ntawm cov khoom yog qhov sib txawv ntawm nws qhov kev txav chaw ntawm qhov chaw muab, peb tseem tuaj yeem hais tias "2 meters/thib ob "yog kwv yees tus nqi ntawm kev nrawm nrawm ntawm t = 1.
Txoj Kev 3 ntawm 3: Cov Lus Nug Piv Txwv
Kauj Ruam 1. Nrhiav tus nqi ntawm qhov nrawm nrawm ntawm t = 4, los ntawm qhov kev hloov chaw s = 5t3 - 3t tsi2 +2t+9.
Qhov teeb meem no zoo ib yam li qhov piv txwv hauv thawj ntu, tshwj tsis yog qhov kev ua zauv no yog kab zauv sib npaug, tsis yog lub zog sib npaug, yog li peb tuaj yeem daws qhov teeb meem no tib yam nkaus.
- Ua ntej, peb coj qhov sib piv ntawm qhov sib npaug:
- Tom qab ntawd, sau tus nqi t (4):
s = 5t3- 3t tsi2+2t+9
s = (3) 5t(3 - 1) - (2) 3t(2 - 1) + (1) 2t(1 - 1) + (0) 9t0 - 1
1 5t qug(2) -6t ib(1) + 2t(0)
1 5t qug(2) -6t + 2
s = 15 hli(2)-6t + 2
15(4)(2)- 6(4) + 2
15(16) - 6(4) + 2
240 - 24 + 2 = 22 meters/thib ob
Kauj Ruam 2. Siv cov duab kwv yees los nrhiav qhov nrawm ntawm (1, 3) rau qhov kev hloov qhov sib npaug s = 4t2 - t.
Txog qhov teeb meem no, peb yuav siv (1, 3) ua tus taw tes P, tab sis peb yuav tsum txhais lwm lub ntsiab lus uas nyob ib sab ntawm qhov ntawd raws li cov lus Q. Tom qab ntawd peb tsuas yog xav txiav txim siab tus nqi H thiab ua qhov kwv yees.
- Ua ntej, nrhiav tus nqi Q ua ntej ntawm t = 2, 1.5, 1.1 thiab 1.01.
- Tom qab ntawd, txiav txim siab tus nqi H:
- Txij li tus nqi H yog ze rau 7, peb tuaj yeem hais qhov ntawd 7m/feebyog kwv yees nrawm nrawm ntawm (1, 3).
s = 4 tsi2- t
t = 2:
s = 4 (2) cov2- (2)
4 (4) - 2 = 16 - 2 = 14, yog li Q = (2,14)
t = 1.5:
s = 4 (1.5) cov2 - (1.5)
4 (2.25) - 1.5 = 9 - 1.5 = 7.5, yog li Q = (1.5, 7.5)
t = 1.1:
s = 4 (1.1)2 - (1.1)
4 (1.21) - 1.1 = 4.84 - 1.1 = 3.74, yog li Q = (1.1, 3.74)
t = 1.01: kuv
s = 4 (1.01)2 - (1.01)
4 (1.0201) - 1.01 = 4.0804 - 1.01 = 3.0704, yog li Q = (1.01, 3.0704)
Q = (2,14):
H = (14 - 3)/(2 - 1)
H = (11)/(1) =
Kauj ruam 11.
Q = (1.5, 7.5):
H = (7.5 - 3)/(1.5 - 1)
H = (4.5)/(. 5) =
Kauj ruam 9.
Q = (1.1, 3.74):
H = (3.74 - 3)/(1.1 - 1)
H = (.74)/(. 1) = 7.3
Q = (1.01, 3.0704):
H = (3.0704 - 3)/(1.01 - 1)
H = (.0704)/(. 01) = 7.04
Lub tswv yim
- Txhawm rau nrhiav tus nqi ntawm kev nrawm (hloov pauv nrawm hauv lub sijhawm), siv tus txheej txheem hauv thawj ntu kom tau txais qhov sib npaug rau qhov ua haujlwm ntawm kev hloov chaw. Tom qab ntawd tsim qhov sib npaug muab rov los, lub sijhawm no los ntawm koj qhov kev ua zauv tau los. Qhov no yuav muab rau koj qhov kev ua zauv kom pom qhov nrawm ntawm txhua lub sijhawm, txhua yam koj yuav tsum ua yog sau koj lub sijhawm.
- Qhov sib npaug cuam tshuam txog tus nqi ntawm Y (kev hloov chaw) mus rau X (lub sijhawm) yuav yooj yim heev, piv txwv li Y = 6x + 3. Hauv qhov no, qhov nqes hav tus nqi yog qhov tsis tu ncua, thiab tsis tas yuav nrhiav cov lej los laij nws, qhov twg raws li qhov sib npaug ntawm kab ncaj, Y = mx + b yuav sib npaug 6.
- Kev txav chaw zoo ib yam li kev nrug deb, tab sis muaj kev qhia, yog li kev hloov chaw yog qhov muaj nuj nqis vector, thaum qhov nrug deb yog qhov ntau. Tus nqi txav chaw tuaj yeem ua rau tsis zoo, tab sis qhov deb yuav ib txwm muaj qhov zoo.
