4.11-bo'lim : Chiziqli taxminlar

1-4-masalalar uchun berilgan nuqtadagi funktsiyaga chiziqli yaqinlashishni toping.

1. \(f\left( x \right) = \cos \left( {2x} \right)\), \(x = \pi \)
2. \(h\left( z \right) = \ln \left( {{z^2} + 5} \right)\), \(z = 2\)
3. \(g\left( x \right) = 2 - 9x - 3{x^2} - {x^3}\), \(x = - 1\)
4. \(g\left( t \right) = {{\bf{e}}^{\sin \left( t \right)}}\), \(t = - 4\)
5. \(y = 0\) da \(h\left( y \right) = \sin \left( {y + 1} \right)\) ga chiziqli yaqinlashishni toping. \(\sin \left( 2 \right)\) va \(\sin \left( {15} \right)\) qiymatini taxmin qilish uchun chiziqli yaqinlashishdan foydalaning. Taxminan qiymatlarni aniq qiymatlar bilan solishtiring.
6. \(t = 32\) da \(R\left( t \right) = \sqrt[5]{t}\) ga chiziqli yaqinlashishni toping. \(\sqrt[5]{{31}}\) va \(\sqrt[5]{3}\) qiymatini taxmin qilish uchun chiziqli yaqinlashuvdan foydalaning. Taxminan qiymatlarni aniq qiymatlar bilan solishtiring.
7. \(x = 1\) da \(h\left( x \right) = {{\bf{e}}^{1 - x}}\) ga chiziqli yaqinlashishni toping. \({\bf{e}}\) va \({{\bf{e}}^{ - 4}}\) qiymatini taxminiy aniqlash uchun chiziqli yaqinlashuvdan foydalaning. Taxminan qiymatlarni aniq qiymatlar bilan solishtiring.

8-10-masalalar uchun berilgan qiymatni chiziqli yaqinlashish yordamida va hech qanday hisoblash yordamidan foydalanmasdan baholang.

1. \(\ln \left( {1.1} \right)\)
2. \(\sqrt {8.9} \)
3. \(\sec \left( {0.1} \right)\)