Question

x趋近于0 求(ln(1+x+x^2)+arcsin3x)/(sin2x+(tanx)^2)的极限 麻烦过程详细点

Answer 1

lim(x→0)(tanx-sinx)/ln(x²+1) =lim(x→0)(x³/2)/ln(x²+1) tanx-sinx~x³/2 =lim(x→0)(3/2)x²/[2x/(x²+1)] 洛必达法则 =lim(x→0)3x(x²+1)/4 =0

Answer 2

属于0/0型，使用罗比塔法则,上下求导
=lim[(1+2x)/(1+x+x^2)+3/√(1-9x^2)]/(2cos2x+2tanx(secx)^2)
带入x→0
=lim(1+3)/(2+0)
=2