Cevaplar

2012-11-08T21:19:57+02:00

bunlar sınavda çıkmaz sanırım önemli konulara çalış ama geometri çıkabili

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2012-11-08T21:23:19+02:00

❇ö❧ü♠ ✶
❊❯❈▲■❉ ❯❩❆❨■◆❉❆ ❉Ü❩●Ü◆
✭❙▼❖❖❚❍✮ ❋❖◆❑❙➑❨❖◆▲❆❘
❚❛♥✙♠ ✶✳✵✳✶✳ k ♥❡❣❛t✐❢ ♦❧♠❛②❛♥ ❜✐r t❛♠s❛②✙ ♦❧s✉♥✳ f : U ! R ❢♦♥❦s✐②♦♥✉
tü♠ ♠❡rt❡❜❡❞❡♥ j k ✐ç✐♥ ❦✙s♠✐ tür❡✈❧❡r✐
@
j
f
@xi1 @xi2
:::@xij
✈❛r ✈❡ ❜✉ ❦✙s♠✐
tür❡✈❧❡r p ♥♦❦t❛s✙♥❞❛ sür❡❦❧✐ ✐s❡ f✬②❡ p ♥♦❦t❛s✙♥❞❛ C
k
❢♦♥❦s✐②♦♥✉ ❞❡♥✐r✳
❊➜❡r f : U ! R k 0 ✐ç✐♥ C
k
✲❢♦♥❦s✐②♦♥✉ ✐s❡ f✬②❡ C
1
✲❢♦♥❦s✐②♦♥✉ ❞❡♥✐r✳
Ör♥❡❦ ✶✳✵✳✶✳ ✶✳
f : R ! R; x 7! f(x) = x
1
3
f
0
(x) =
1
3
x
2
3 ✱ ✶✳ ♠❡rt❡❜❡❞❡♥ tür❡✈✐ ✈❛r ❢❛❦❛t 0 ♥♦❦t❛s✙♥❞❛ sür❡❦❧✐ ❞❡➜✐❧
❞♦❧❛②✙s✙②❧❛ tür❡✈ ♠❡✈❝✉t ❞❡➜✐❧❞✐r✳ f✱ C
0
✲❢♦♥❦s✐②♦♥✉❞✉r ❢❛❦❛t C
1
✲❢♦♥❦s✐②♦♥✉
❞❡➜✐❧❞✐r✳
✷✳
g : R ! R; x 7! g(x) =
Z x
0
f(t)dt =
Z x
0
t
1
3 dt
g
0
(x) = f(x) = x
1
3 g✱ C
1
✲❢♦♥❦s✐②♦♥✉❞✉r✳
✸✳ R ü③❡r✐♥❞❡❦✐ ♣♦❧✐♥♦♠✱ s✐♥üs✱ ❦♦s✐♥üs✱ üst❡❧ ❢♦♥❦s✐②♦♥❧❛r✙ C
1
✲❢♦♥❦s✐②♦♥✉❞✉r✳
❚❛♥✙♠ ✶✳✵✳✷✳ ❇✐r ❢♦♥❦s✐②♦♥✉ p ♥♦❦t❛s✙♥✙♥ ❦♦♠➩✉❧✉➜✉♥❞❛ ❜✉ ❢♦♥❦s✐②♦♥✉♥
❚❛②❧♦r s❡r✐s✐♥❡ ❡➩✐t ✐s❡ ✭②❛♥✐ ❜✐r ❢♦♥❦s✐②♦♥ ❚❛②❧♦r s❡r✐s✐♥❡ ❛ç✙❧❛❜✐❧✐②♦rs❛✮
f✬②❡ (p 2 R) p ♥♦❦t❛s✙♥❞❛ ❛♥❛❧✐t✐❦t✐r ❞❡♥✐r✳
➬♦❦ ❞❡➜✐➩❦❡♥❧✐ ❢♦♥❦s✐②♦♥✉♥ ❚❛②❧♦r s❡r✐s✐✿
f(x) = f(p) +
X
i
@f
@xi
(xi pi) +
1
2!
X
i;j
@
2
f
@[email protected]
(xi pi)(xj pj ) + :::

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