lim _(xarrow y)dfrac (1-xy)({x)^2+(y)^2}-|||-bigcirc (3) lim 1-√(xy+1)-|||-y)→(0,0) xy-|||-④ lim _((x,y)arrow (0,0))(xsin dfrac (1)(y)+ysin dfrac (1)(x))-|||-(2)设 =sin (xy)+cos ((y)^2), 求 dfrac (partial z)(partial x),dfrac (partial z)(partial y)-|||-(3)设 =(e)^usin v =x+y =x-y, 求 dfrac (partial z)(partial x),dfrac (partial z)(partial y)-|||-(4)设 =(e)^x+y =sin t =(t)^2, 求 dfrac (dz)(dt).-|||-(5)设 =3(x)^2y+3x(y)^2-2xy, 求 dfrac ({a)^2z}(a{x)^2}, dfrac ({partial )^2z}(partial xpartial y) dfrac ({partial )^2z}(partial {y)^2}.-|||-(6)设函数 z=z(x,y) 由方程 ^x=2xy+3yz+zx 所确定,求 dfrac (partial z)(partial x) dfrac (partial z)(partial y).-|||-(7)求函数 (x,y)=(x)^3+3(y)^2-6xy+1 的极值.-|||-(8)求曲线 x=t+1 =3(t)^2, =(t)^3-1 在点(2,0,0)处的切线与法平面方程-|||-(9)求曲面 ^x=2z-xy+5 在点(1,4,0)处的切平面及法线方程.-|||-(10)交换下列积分次序:4.计算题.-|||-(1)求极限:-|||-① y)→(0,0) x^2y^2 e^xy-|||-lim 1-cos(xy )-|||-0,-|||-② . lim _(xarrow y)dfrac (1-xy)({x)^2+(y)^2}-|||-bigcirc (3) lim 1-√(xy+1)-|||-y)→(0,0) xy-|||-④ lim _((x,y)arrow (0,0))(xsin dfrac (1)(y)+ysin dfrac (1)(x))-|||-(2)设 =sin (xy)+cos ((y)^2), 求 dfrac (partial z)(partial x),dfrac (partial z)(partial y)-|||-(3)设 =(e)^usin v =x+y =x-y, 求 dfrac (partial z)(partial x),dfrac (partial z)(partial y)-|||-(4)设 =(e)^x+y =sin t =(t)^2, 求 dfrac (dz)(dt).-|||-(5)设 =3(x)^2y+3x(y)^2-2xy, 求 dfrac ({a)^2z}(a{x)^2}, dfrac ({partial )^2z}(partial xpartial y) dfrac ({partial )^2z}(partial {y)^2}.-|||-(6)设函数 z=z(x,y) 由方程 ^x=2xy+3yz+zx 所确定,求 dfrac (partial z)(partial x) dfrac (partial z)(partial y).-|||-(7)求函数 (x,y)=(x)^3+3(y)^2-6xy+1 的极值.-|||-(8)求曲线 x=t+1 =3(t)^2, =(t)^3-1 在点(2,0,0)处的切线与法平面方程-|||-(9)求曲面 ^x=2z-xy+5 在点(1,4,0)处的切平面及法线方程.-|||-(10)交换下列积分次序: