Differentsialning asosiy xossasi




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Differentsialning asosiy xossasi
Agar funksiya M0 nuqtada differensiallanuvchi bo`lsa, u holda cheksiz kichik lar uchun

bajariladi, ya`ni
.
Bir necha o`zgaruvchili funksiya uchun taqribiy hisoblash formulasi quyidagi ko`rinishga ega:
.
7-misol. 1,022,01 ni taqribiy hisoblang.
Yechish. z = xy funksiyani qaraymiz. Uning M0(1; 2) nuqtadagi qiymati z(M0)= 1= 1 ga teng.
z = xy funksiyaning to`liq differensialini topamiz:
dz = y xy-1 x + xlnx y
x = 1, y = 2, x = 0,02 va y = 0,01 ga teng. Shuning uchun
dz = 2  13  0,02 + 12  ln1  0,01 = 0,04.
U holda (1,02)2,01(M0) + dz = 1 + 0,04 = 1,04.
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