lim(x趋近于正无穷)(根号(x^2+2)+2x)^2/(3x^2+1)

问题描述:

lim(x趋近于正无穷)(根号(x^2+2)+2x)^2/(3x^2+1)

原式=lim[x²+2+4x√(x²+2)+4x²]/(3x²+1)
=lim[5x²+2+4x√(x²+2)]/(3x²+1)
上下除以x²
=lim[5+2/x²+4√(1+1/x²)]/(3+1/x²)
=(5+4√1)/3
=3