x*e^(-x^2)和x/(1+x-2x^2)展开成x的幂级数x*e^(-x^2)和x/(1+x-2x^2)如何展开成幂级数一直没有弄懂

(X^2-X)E^(1-X)求导 (1-e^(x^2))/x 2e^(x-1),x e^x+(x-3)e^x =[1+(x-3)]e^x =(x-2)e^x f(x)=x(e^x-1)-1/2 x lim(x→0)e^x-x-1/x^2 ∫ e^x-e^(-x)dx=e^x+e^(-x)|=e+1/e-2 1/[(e^x+e^-x)^2]不定积分 ∫ e^x/e^2x+1 怎么证明D(X)=E(X^2)-[E(X)]^2和D(X)=E[X-E(X)]^2 关于极限1.lim((x^-1) + (x^-4))/((x^-2) - (x^-3)) x-> 正无穷2.lim ((e^x) - (e^-x))/((e^x) + (e^-x)) x-> 负无穷 已知x=1是函数f(x)=(x^2+ax)e^x,x>0和bx ,x lim(x→0)[e^x-e^(2x)]/x f(x)={(1-e^x)/sin(x/2) ,x>0 ;ae^2x,x x*e^(-x^2)和x/(1+x-2x^2)展开成x的幂级数x*e^(-x^2)和x/(1+x-2x^2)如何展开成幂级数一直没有弄懂 积分e^(x-x^2), *-----------------------------------------------*| 6 4 X | 8 X X | X X 5 || X X X | X X X | X 7 8 || X X X | X X X | X X X ||---------------+---------------+--------------- || X X X | X X X | 5 1 X || X X X | X 6 X | X X X || 8 X X | 3 5 X | 2 X X || e^x/1+2e^2x不定积分,e^x/(1+2e^2x)