We have
`underset(xtooo)lim(sqrt(25x^(2)-3x)+5x)" "(oo-oo"form")`
`=underset(ytooo)lim(sqrt(25y^(2)+3y)-5y),"where "y=-x`
`=underset(ytooo)lim(25y^(2)+3y-25y^(2))/(sqrt(25y^(2)+3y)+5y)`
`=underset(ytooo)lim(3y)/(sqrt(25y^(2)+3y)+5y)`
`=underset(ytooo)lim(3)/(sqrt(25+(3)/(y))+5)=(3)/(5+5)=(3)/(10)`
