Question

高等数学试题，求大神帮忙解答，要详细过程

高等数学试题，求大神帮忙解答，要详细过程

Answer 1

解：原式=lim(x->0)[2x*arctan(x²)/(4x³)] (0/0型极限，应用罗比达法则)
=(1/2)lim(x->0)[arctan(x²)/x²]
=(1/2)lim(x->0)[(2x/(1+x^4))/(2x)] (0/0型极限，应用罗比达法则)
=(1/2)lim(x->0)[1/(1+x^4)]
=(1/2)*(1/(1+0))
=1/2。