求极限lim(x→∞,y→∞)(x+y)/(x²+y²)的值为

• 求极限lim(x→∞,y→∞)(x+y)/(x²+y²)的值为
• 求极限，x，y趋于无穷（x＋y）/（x²＋y²＋1）的极限
• 求极限lim(x y )/(x ²+y ²)当x ,y 都趋近0!
• 求极限lim(x,y)→(0,0)xy\x²+y²

求极限lim(x→∞,y→∞)(x+y)/(x²+y²)的值为

∵x²+y²≥2│xy│

∴│(x+y)/(x²+y²)│

≤│(x+y)/(2xy)│

=│(1/x+1/y)/2│

lim(x→∞,y→∞)│(x+y)/(x²+y²)│

≤lim(x→∞,y→∞)│(1/x+1/y)/2│=0

∴lim(x→∞,y→∞)(x+y)/(x²+y²)=0

求极限，x，y趋于无穷（x＋y）/（x²＋y²＋1）的极限

∵x +y +1≥2│xy│+1≥2│xy│

∴│(x+y)/(x +y +1)│

≤│(x+y)/(2xy)│

=│(1/x+1/y)/2│

∴0≤│(x+y)/(x +y +1)│≤│(1/x+1/y)/2│

0≤lim(x→∞,y→∞)│(x+y)/(x +y )+1│≤lim(x→∞,y→∞)│(1/x+1/y)/2│=0

∴lim(x→∞,y→∞)(x+y)/(x +y )=0

求极限lim(x y )/(x ²+y ²)当x ,y 都趋近0!

都不存在！y ＝k x 代就化简单得k /(1＋k ²)!k 是变量！

求极限lim(x,y)→(0,0)xy\x²+y²

极限不存在

假设以y＝kx趋近(0,0)

原极限

＝lim{x，y→0}kx^2/[(k^2+1)x^2]

＝k/(k^2+1)

显然k不同极限不同，所以极限不存在