Limit 1 2 3 4 Uyar Sadan limit
- Slides: 117
Limit 1
2
3
4
Uyarı: Sağdan limit, soldan limite; eşit ise fonksiyonun limiti vardır. eşit değilse fonksiyonun limiti yoktur. 5
6
7
8
9
10
Limitin Özellikleri 1) 2) 3) 11
4) 5) 6) 12
13
14
yu u n o k k u e b s i r şla z a e d a m Ark r et tabiliriz a u r k n e u t ak c u çab 15
16
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23
Kritik Noktalar a) Kesirli fonksiyonlarda paydayı sıfır yapan değerler b) Parçalı fonksiyonlarda fonksiyonun kuralının değiştiği noktalar c) Mutlak değer fonksiyonunda içeriyi sıfır yapan değer 24
25
26
Trigonometrik Fonksiyonların limiti A H e ot ip s nü Karşı . B Komşu C 27
sin 0 1 cos 1 0 tan 0 1 tanımsız cot tanımsız 1 0 28
Kurallar 1) 2) 3) 4) 29
5) 6) 7) 8) 30
Uyarı: ve dır. 31
32
33
34
35
36
37
Not: 38
1) 2) 3) 4) 39
40
41
42
43
44
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46
47
a) Pay ile paydanın derecesi aynı ise, büyük dereceli ifadelerin katsayıları birbirine oranlanır. b) c) Paydanın derecesi büyük ise, sonuç 0 dır. 48
1) 2) 3) 49
4) 5) 6) 50
7) 8) 9) 51
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55
56
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62
63
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67
ALIŞTIRMALAR 68
69
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71
72
Örnek: 73
74
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76
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78
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108
AÇIK ÖĞRETİM SINAVLARINDA ÇIKMIŞ LİMİT SORULARI 109
SORU 1: 110
SORU 2: 111
SORU 3: 112
SORU 4: 113
114
115
116
117
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