一道极限题目lim(x→0)sinx+xf(x)/x^3=1/2 求f(0),f`(0),f``(0)
问题描述：
一道极限题目
lim(x→0)sinx+xf(x)/x^3=1/2 求f(0),f`(0),f``(0)
答
用泰勒公式展开法,在 x=0 点sinx=x-1/3!*x^3+o(x^4)f(x)=f(0)+f'(0)*x+f''(0)/2!*x^2+o(x^3)那么 (sinx+xf(x))/x^3=(x-1/3!*x^3+o(x^4)+f(0)*x+f'(0)*x^2+f''(0)/2!*x^3+o(x^4))/x^3=(1+f(0))*x+f'(0)*x^2+(f''(0)/2...