求(x,y)趋近于(0,0)时,lim((x^3)+(x^2)y+x(y^2)+(y^3))/((x^2)-xy+(y^
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/14 01:04:44
求(x,y)趋近于(0,0)时,lim((x^3)+(x^2)y+x(y^2)+(y^3))/((x^2)-xy+(y^2))
令:x=rcosθ ,y=rsinθ
lim[(x,y)->(0,0)] ((x^3)+(x^2)y+x(y^2)+(y^3))/((x^2)-xy+(y^2))
=lim[(x,y)->(0,0)] (r^3*(sinθ+cosθ)/(r^2-r^2sinθcosθ)
=lim[(x,y)->(0,0)] r* {(sinθ+cosθ)/(1-sinθcosθ)}
=lim[(x,y)->(0,0)] r* {(sinθ+cosθ)/(1-1/2*sin2θ)}
∵ 1/2 ≤ |1-1/2*sin2θ| ; |{(sinθ+cosθ)/(1-1/2*sin2θ)}|≤2/(1/2)=4
=0
lim[(x,y)->(0,0)] ((x^3)+(x^2)y+x(y^2)+(y^3))/((x^2)-xy+(y^2))
=lim[(x,y)->(0,0)] (r^3*(sinθ+cosθ)/(r^2-r^2sinθcosθ)
=lim[(x,y)->(0,0)] r* {(sinθ+cosθ)/(1-sinθcosθ)}
=lim[(x,y)->(0,0)] r* {(sinθ+cosθ)/(1-1/2*sin2θ)}
∵ 1/2 ≤ |1-1/2*sin2θ| ; |{(sinθ+cosθ)/(1-1/2*sin2θ)}|≤2/(1/2)=4
=0
求(x,y)趋近于(0,0)时,lim((x^3)+(x^2)y+x(y^2)+(y^3))/((x^2)-xy+(y^
求极限lim(y-x)x/根号下(x^2+y^2) x,y趋近于0
lim(xy/(x^2+y^2))^x^2 x,y趋近无穷 求极限
求二元函数极限:(x,y)趋近于(2,-1/2)时lim(2+xy)^(1/(y+xy^2))
微积分极限问题LIM X趋近于0 Y趋近于2 X的平方乘以Y 除以 X的4次方 + Y的平方 求极限 当XY沿曲线Y=K
已知3x^2+xy-2y^2=0,求{(x+y)/(x-y)+4xy/(y^2-x^2)}/{(x+3y)*(x-y)}
已知x-3y=0,求(2x+y)/(x^2-2xy+y^2)X(x-y)
已知3x*+xy-2y*=0,求(x/y)-(y/x)-(x*+y*)/(xy)的值.*是平方
已知x*x-4xy+4y*y=0 求[2x(x+y)-y(x+y)]/(4x*x-4xy+y*y)的值?
若2x平方+3xy-2y平方=0,求x+y/x-y
|x+2y+3|+(2x+y)²=0求x²-xy+y²
求极限:xy/(x^2+y^2),x和y同时趋近于零