lim(x->0)((x-arcsinx)/(tanx)^3)
问题描述：
lim(x->0)((x-arcsinx)/(tanx)^3)
答
根据等价无穷小和泰勒展开
原式=lim(x->0) (x-( x + 1/2*x^3/3 + 1*3/(2*4)*x^5/5 + ... ))/x^3
=lim(x->0) -1/6+o(x^2)
=-1/6
答
lim(x->0)((x-arcsinx)/(tanx)^3)=lim(x->0)((x-arcsinx)/x³=lim(x->0)((1-1/√1-x²)/3x²=lim(x->0)((√1-x²-1)/3x²√1-x²=1/3lim(x->0)((√1-x²-1)/x²=1/3lim(x->0)(-x...