Limit[(Sqrt[x^2+x+1]-1)/Sin[2x],x->0]

Question

Limit[(Sqrt[x^2 + x + 1] - 1)/Sin[2 x],x -> 0]

Answer 1

上下乘√(x²+x+1)+1
原式=lim(x²+x)/sin2x[√(x²+x+1)+1]
除以2x
=1/2*lim(1+x)/（sin2x/2x)[√(x²+x+1)+1]
=1/2*1/(1*2)
=1/4