`lim_(x->+infty)(xsqrt(4x^2+9)+2x)`
`=lim_(x->+infty)[xsqrt(x^2(4+9/x^2))+2x]`
`=lim_(x->+infty)(x^2sqrt(4+9/x^2)+2x)`
`=lim_(x->+infty)[x(xsqrt(4+9/x^2)+2)]`
`=lim_(x->+infty){x[x(sqrt(4+9/x^2)+2/x)]}`
`=lim_(x->+infty)[x^2(sqrt(4+9/x^2)+2/x)]` `(1)`
Ta có:
`lim_(x->+infty)x^2=+infty`
`lim_(x->+infty)sqrt(4+9/x^2)+2/x=sqrt4=2`
`->(1)=+infty.2=+infty`