函数f(x)=e^x/2在x=0处的泰勒级数为____．

函数f(x)=e^x/2在x=0处的泰勒级数为____．

1+x/2+x²/2!2²+…+xⁿ/n!2ⁿ+…. 解析: f(x)=e^x/2 f⁽ⁿ⁾(x)=(1/2ⁿ)e^(x/2) f⁽ⁿ⁾(0)=1/2′′ ∴f(x)=e^(x/2)在x=0处的泰勒级数为： 1+(1/2)x+1/2!•(1/2²)x²+1/3!•(1/2³)x³+…+1/n!•(1/2ⁿ)xⁿ+…