4.11-bo'lim: Chiziqli taxminlar

1 va 2-masalalar uchun funksiyaning berilgan nuqtadagi chiziqli yaqinligini toping.

1. \(f\left( x \right) = 3x\,{{\bf{e}}^{2x - 10}}\) at \(x = 5\) Yechim
2. \(h\left( t \right) = {t^4} - 6{t^3} + 3t - 7\) at \(t = - 3\) Yechim
3. \(z = 2\) da \(g\left( z \right) = \sqrt[4]{z}\) ga chiziqli yaqinlashishni toping. \(\sqrt[4]{3}\) va \(\sqrt[4]{{10}}\) qiymatini taxminiy aniqlash uchun chiziqli yaqinlashuvdan foydalaning. Taxminan qiymatlarni aniq qiymatlar bilan solishtiring. Yechim
4. \(t = \frac{1}{2}\) da \(f\left( t \right) = \cos \left( {2t} \right)\) ga chiziqli yaqinlashishni toping. \(\cos \left( 2 \right)\) va \(\cos \left( 18 \right)\) qiymatini taxmin qilish uchun chiziqli yaqinlashishdan foydalaning. Taxminan qiymatlarni aniq qiymatlar bilan solishtiring. Yechim
5. Hech qanday hisoblash yordamidan foydalanmasdan \({{\bf{e}}^{0.1}}\) qiymatini taxmin qilish uchun chiziqli yaqinlashuvdan foydalaning. Yechim