10.16-bo'lim : Teylor seriyasi

1-3-muammolar uchun berilgan funksiya uchun Teylor seriyasini aniqlash uchun eslatmalarda keltirilgan Teylor seriyalaridan birini ishlating.

1. \(f\left( x \right) = \sin \left( {{x^4}} \right)\) \(x = 0\) haqida
2. \(f\left( x \right) = 9{x^4}{{\bf{e}}^{ - 12x}}\) \(x = 0\) haqida
3. \(f\left( x \right) = 6{x^2}\cos \left( {7{x^5}} \right)\) \(x = 0\) haqida

4-13-muammo uchun quyidagi funksiyalarning har biri uchun Teylor seriyasini toping.

1. \(f\left( x \right) = \sin \left( x \right)\) \(\displaystyle x = \frac{{3\pi }}{2}\) haqida
2. \(f\left( x \right) = {{\bf{e}}^{1 - 8x}}\) \(x = 3\) haqida
3. \(f\left( x \right) = \ln \left( {1 - x} \right)\) \(x = - 2\) haqida
4. \(f\left( x \right) = \ln \left( {2 + 9x} \right)\) \(x = 1\) haqida
5. \(\displaystyle f\left( x \right) = \frac{1}{{{{\left( {6 - x} \right)}^7}}}\) \(x = 4\) haqida
6. \(\displaystyle f\left( x \right) = \frac{1}{{{{\left( {4 + 9x} \right)}^2}}}\) \(x = - 2\) haqida
7. \(f\left( x \right) = \sqrt {2 + x} \) \(x = 1\) haqida
8. \(f\left( x \right) = \sqrt {1 - 4x} \) \(x = - 3\) haqida
9. \(f\left( x \right) = - 3{x^2} - x + 10\) \(x = - 8\) haqida
10. \(f\left( x \right) = {x^3} + 9{x^2} - 10x + 2\) \(x = 3\) haqida