函数f(x)=ex/2在x=0处的泰勒级数为____．
1+x/2+x2/2!22+…+xn/n!2n+…. 解析: f(x)=ex/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+…
函数f(x)=ex/2在x=0处的泰勒级数为____．
1+x/2+x2/2!22+…+xn/n!2n+…. 解析: f(x)=ex/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+…
