Og`ma asimptota. Og`ma asimptota tenglamasini y=kx+b ko`rinishda izlaymiz. Bir xil abssissali egri chiziq ordinatasi va
asimptota ordinatasi orasidagi masofa x®+¥ yoki x®-¥ da nolga intilishini ko`rsatamiz. 39-rasm
F araz qilaylik, M va N abssissasi x ga teng bo`lgan egri chiziqdagi va asimptotadagi nuqtalar, (40-rasm) MP esa M nuqtadan asimptotagacha bo`lgan masofa, a (a¹p/2) asimptotaning Ox o`qining musbat yo`nalishi bilan hosil qilgan burchagi bo`lsin. U holda DMNP uchburchakdan MP=MNcosa, bundan esa
MN=MP/cosa
tenglikkaegabo`lamiz. Bu
tenglikdan, agar MP nolga intilsa, u holda MN ham nolga intilishi, va aksincha, agar MN nolga intilsa, u holda MP nolga intilishi kelib chiqadi.
Shunday qilib, agar x®+¥ yoki x® -¥ da
40-rasm
f(x)-kx-b ayirma nolga intilsa, u holda y=kx+b to`g`ri chiziq y=f(x) funksiya grafigining asimptotasi bo`lar ekan.
Bundan ![](data:image/png;base64,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) (f(x)-kx-b)=0 shart y=kx+b to`g`ri chiziqning y=f(x) funksiya grafigining og`ma asimptotasi bo`lishi uchun zaruriy va yetarli shart ekanligi kelib chiqadi.
Xususan, y=b gorizontal asimptota bo`lishi uchun (f(x)-b)=0, ya`ni f(x)=b shartning bajarilishi zarur va yetarli.
Amalda og`ma asimptotalarni topish uchun quyidagi teoremadan foydalaniladi.
Do'stlaringiz bilan baham: |