4.13-bo'lim: Nyuton usuli

1 va 2-masalalar uchun Nyuton usulidan foydalanib, berilgan funktsiya va \({x_0}\) ning berilgan qiymati uchun \({x_{\,2}}\) ni aniqlang.

1. \(f\left( x \right) = {x^3} - 7{x^2} + 8x - 3\), \({x_{\,0}} = 5\) Yechim
2. \(f\left( x \right) = x\cos \left( x \right) - {x^2}\), \({x_{\,0}} = 1\) Yechim

3 va 4-masalalar uchun Nyuton usulidan foydalanib, berilgan tenglamaning oltita kasrgacha aniq, berilgan oraliqda joylashgan ildizini toping.

1. \({x^4} - 5{x^3} + 9x + 3 = 0\) in \(\left[ {4,6} \right]\) Yechim
2. \(2{x^2} + 5 = {{\bf{e}}^x}\) in \(\left[ {3,4} \right]\) Yechim

5 va 6-masalalar uchun Nyuton usulidan foydalanib, berilgan tenglamaning barcha ildizlarini oltita kasrgacha aniq toping.

1. \({x^3} - {x^2} - 15x + 1 = 0\) Yechim
2. \(2 - {x^2} = \sin \left( x \right)\) Yechim