f(x)=x∧2 sinx展开为x的幂级数,其含x∧7项的系数

题目

f(x)=x∧2 sinx展开为x的幂级数,其含x∧7项的系数

答案

g(x) = sinxg'(x) = cosxg''(x) = -sinxg'''(x)= -cosxg''''(x) = sinxg'''''(x) = cosxg(x) = g(0) +(g'(0)/1!)x +(g''(0)/2!)x^2+.f(x) = x^2.sinx= g(0) x^2+(g'(0)/1!)x^3 +(g''(0)/2!)x^4+.coef.of x^7=g^(5)(0...