- 泰勒公式问题按x
- 按x-4的乘幂展开该多项式。请写出详细过程,不胜谢谢
- f(x)=x^4-5x^3+x^-3x+4...........f(4)=-56
--->f'(x)=4x^3-15x^+2x-3........f'(4)=21
--->f''(x)=12x^-30x+2...........f''(4)=74
--->f'''(x)=24x-30..............f'''(4)=66
--->f''''(x)=24.................f''''(4)=24
--->f<5>(x)=f<6>(x)=...=0
由Taylor公式:
f(x)=f(4)+[f'(4)/1!](x-4)+[f''(4)/2!](x-4)^+
+[f'''(4)/3!](x-4)^3+[f''''(4)/4!](x-4)^4
=-56+21(x-4)+34(x-4)^+11(x-4)^3+(x-4)^4