10.17-bo'lim: Seriya ilovalari

1. Quyidagi integral uchun \(x = 0\) haqida Teylor seriyasini aniqlang. \[\int{{\frac{{{{\bf{e}}^x} - 1}}{x}\,dx}}\] Yechim
2. \(x = - 4\) haqidagi \(f\left( x \right) = {{\bf{e}}^{ - 6x}}\) ning Teylor seriyasi uchun \({T_2}\left( x \right)\), \({T_3}\left( x \right)\) va \({T_4}\left( x \right)\) ni yozib oling. \(\left[ { - 8, - 2} \right]\) oralig'i uchun bir xil grafikda Teylor ko'phadlari va \(f\left( x \right)\)ning uchtasini chizing. Yechim
3. \(x = 0\) haqidagi \(f\left( x \right) = \ln \left( {3 + 4x} \right)\) Teylor seriyasi uchun \({T_3}\left( x \right)\), \({T_4}\left( x \right)\) va \({T_5}\left( x \right)\) ni yozib oling. \(\left[ {\displaystyle - \frac{1}{2},2} \right]\) oralig'i uchun bir xil grafikda Teylor ko'phadlari va \(f\left( x \right)\)ning uchtasini chizing. Yechim