Question

函数f（x）＝x∧3＋4x∧2＋5在x＝1处的n阶泰勒公式

Answer 1

令t=x-1
则x=t+1
f(x)=(t+1)^3+4(t+1)^2+5
=t^3+3t^2+3t+1+4t^2+8t+4+5
=t^3+7t^2+11t+10
=(x-1)^3+7(x-1)^2+11(x-1)+10
这就是在x=1处的泰勒展开式.