求极限lim(3-根号下x^2+y^2+9)/(x^2+y^2),x→0,y→0

题目

求极限lim(3-根号下x^2+y^2+9)/(x^2+y^2),x→0,y→0

答案

lim(x→0,y→0)[3-√(x^2+y^2+9]/(x^2+y^2)=lim(x→0,y→0)[9-((x^2+y^2+9)]/(x^2+y^2)[3+√(x^2+y^2+9)]=lim(x→0,y→0)(-1)/[3+√(x^2+y^2+9)]=-1/6