搜搜考试网lim （x,y）->(0,0) xy/[根号下(xy+1)]-1的值为
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/08/09 03:51:00
lim （x,y）->(0,0) xy/[根号下(xy+1)]-1的值为
![lim （x,y）->(0,0) xy/[根号下(xy+1)]-1的值为](/uploads/image/z/6744109-13-9.jpg?t=lim+%EF%BC%88x%2Cy%EF%BC%89-%26gt%3B%280%2C0%29+xy%2F%5B%E6%A0%B9%E5%8F%B7%E4%B8%8B%28xy%2B1%29%5D-1%E7%9A%84%E5%80%BC%E4%B8%BA)
x^2+(y^2)/2=1,
x^2+[(1/√2)y]^2=1,
设x=cosA,y=√2sinA,
因x＞0,y＞0,不妨设0＜A＜π/2,
x√(1+y^2)=cosA√[1+2(sinA)^2]
=√{(cosA)^2[1+2(sinA)^2]}
=√{[1-(sinA)^2][1+2(sinA)^2]}
=√[1+(sinA)^2-2(sinA)^4]
=√{1+(1/√2)[√2(sinA)^2]-[√2(sinA)^2]^2}
=√{-[√2(sinA)^2-1/(2√2)]^2+[1/(2√2)]^2+1}
=√{-[√2(sinA)^2-√2/4]^2+9/8}
=√{-2[(sinA)^2-1/4]^2+9/8}
=√{-2[(sinA+1/2)(sinA-1/2)]^2+9/8}
≤√(9/8)=(3/4)√2
当sinA=1/2,即x=y=√2/2时,原式取最大值(3/4)√2.
x^2+[(1/√2)y]^2=1,
设x=cosA,y=√2sinA,
因x＞0,y＞0,不妨设0＜A＜π/2,
x√(1+y^2)=cosA√[1+2(sinA)^2]
=√{(cosA)^2[1+2(sinA)^2]}
=√{[1-(sinA)^2][1+2(sinA)^2]}
=√[1+(sinA)^2-2(sinA)^4]
=√{1+(1/√2)[√2(sinA)^2]-[√2(sinA)^2]^2}
=√{-[√2(sinA)^2-1/(2√2)]^2+[1/(2√2)]^2+1}
=√{-[√2(sinA)^2-√2/4]^2+9/8}
=√{-2[(sinA)^2-1/4]^2+9/8}
=√{-2[(sinA+1/2)(sinA-1/2)]^2+9/8}
≤√(9/8)=(3/4)√2
当sinA=1/2,即x=y=√2/2时,原式取最大值(3/4)√2.
lim （x,y）->(0,0) xy/[根号下(xy+1)]-1的值为
lim （x,y）->(0,0) xy/[根号下(xy+1)]-1的值为
若(1)xy>0,(2)xy<0,求|x|/x+|y|+|xy|/xy的值
求极限lim x→0 y→0 2xy/根号下1+xy 然后-1 {不在根号里｝
lim(x,y)-(0,0)=根号下(xy+9)-3/xy
若X>0,y>0,且x-根号下xy-2y=0,求(2x-根号下xy)/y+2根号下xy的值
若x>0,y>0,且x-根号下xy-2y=0,求【2x-根号下xy】÷【y+2根号下xy】的值
求细细讲解1.2.已知x>0,y>0且x-2根号下xy-15y=0,则2x+根号下xy+3y除以x+根号下x
已知根号下4x-5y与根号下x-y-1互为相反数,则根号下xy-根号下x/y的值为
求极限:lim xy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)
若实数xy满足根号下x+1+(y-5)²则xy的次方值为?
数学极限计算lim（x,y）→（0,0） xy/ [√(2-e^xy）-1]= lim（x,y）→（0,0） -xy/（