limx->0,y->2(x y-2 根号下x 1-根号下3-y)
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2y+3x=2xy(2y+3x)/(2xy)=1(1/x)+(3/y)=11≥2√(3/(xy))1≥12/(xy)xy≥12xy的最小值是12
由y=3xy+x得x-y=-3xy2x+5xy-2y/x-2xy-y=2(x-y)+5xy/x-y-2xy=-6xy+5xy/-3xy-2xy1/5
对.前提是x不等于y
y-x-2xy=0y-x=2xyx-y=-2xy(3x+xy-3y)/(y-xy-x)=[3(x-y)+xy]/[(y-x)-xy]=(-6xy+xy)/(2xy-xy)=-5xy/xy=-5
x=-2y(2xy+y^2)/(x^2-xy)=(-4y^2+y^2)/(4y^2+2y^2)=-3y^2/(6y^2)=-1/2再问:我算出来也是-1/2,可答案说是-15/28
解(x+1)平方+/y-1/=0∴x+1=0,y-1=0∴x=-1,y=1∴2(xy-5xy平方)-(3xy平方-xy)=(2xy+xy)+(-10xy平方-3xy平方)=3xy-13xy平方=3×(
由limx→0,y→0f(x,y)-xy(x2+y2)2=1知,因此分母的极限趋于0,故分子的极限必为零,从而有f(0,0)=0;因为极限等于1;故f(x,y)-xy~(x2+y2)2(|x|,|y|
这个是原题要求的吧|x|/x+|y|/y+|xy|/xy(1)xy>0x,y都大于零或都小于零x,y都大于零时|x|/x+|y|/y+|xy|/xy=|x|/x+|y|/y+|xy|/xy=x/x+y
因为x+2y=0,所以x=-2y原式=(x^2+2xy)/(xy+y^2)=(4y^2-4Y^2)/(-3y^2+y^2)=0/(-2y^2)又因为xy不等于零,所以x、y君不等于零,所以-2y^2亦
xy(y-2)+2(y-2)下步不写了能看懂吧?
伯努利方程xy'+y=2y^3->x/y^3*y'+1/y^2=2令1/y^2=t-x/2*dt/dx+t=2解这个一阶方程得(2x^(-2)+c)*x^2
直接将x=2y=0代入其中,得ln(2+e*0)/根号2*2+0*2)=ln3/2
x+2y=0,xy不等于0∴x=-2yx²+2xy/xy+y²=(4y²-4y²)/(-2y²+y²)=0
y-x-2xy=0所以x-y=-2xyy-x=2xy所以原式=[3(x-y)+xy]\[(y-x)-xy]=[3×(-2xy)+xy]\(2xy-xy)=-5xy\xy=-5
x+2y+xy=3030-xy=x+2y≥2√2xy即xy+2√2xy-30≤0解得-5√2≤√xy≤3√2xy≤18xy的最大值是18
x²+y²-xy+2x-y+1=[3(x+1)²+(x-2y+1)²]/4=0,由于(x+1)²>=0且(x-2y+1)²>=0,则有x+1
lim(x→0)sin3x/2x=lim(x→0)(sin3x/3x)*(3/2)=lim(3x→0)(sin3x/3x)*(3/2)lim(x→0)sinx/x=1=3/2
x+y=5xy(2x-3xy+2y)/(x+2xy+y)=[2(x+y)-3xy]/[(x+y)+2xy]=(2×5xy-3xy)/(5xy+2xy)=7xy/7xy=1再问:若x+1/x=3,求(x
x²-7xy+12y²=0(x-3y)(x-4y)=0x1=3yx2=4yx=3y时原式=9y²-3y²+y²/6y²=7/6x=4y时原式
∵x-y=4xy∴原式=[2(x-y)+3xy]/[-(x-y)-2xy]=(8xy+3xy)/(-4xy-2xy)=11xy/(-6xy)=-11/6