x→0,y→0[2-√(xy+4)]/xy的极限.x→2,y→0sin(xy)/y的极限
举一反三
- 下列方程中( )是一阶线性微分方程。 A: \( 2{x^2}yy' = {y^2} + 1 \) B: \( xy' + {y \over x} - x = 0 \) C: \( \cos y + x\sin y { { dy} \over {dx}} = 0 \) D: \( y'' + xy' = 4{x^2} + 1 \)
- 分解因式()x()3()y()-()2()x()2()y()2()+()xy()3()正确的是A.()xy()(()x()+()y())()2()B.()xy()(()x()2()﹣()2()xy()+()y()2())()C.()xy()(()x()2()+2()xy()﹣()y()2())()D.()xy()(()x()﹣()y())()2
- 下列方程中( )是微分方程。 A: \( x{y^3} + 2{y^2} + {x^2}y = 0 \) B: \( {y^2} + xy - y = 0 \) C: \( x + {y^2} = 0 \) D: \( dy + ydx = 0 \)
- (多选)以下平面弹性体的位移或形变状态不可能存在的是 A: 位移分量$u = {k_1}\left( {{x^2} + {y^2}} \right),v = {k_2}xy$(${k_1},{k_2}$为常数) B: ${\varepsilon _x} = k\left( {{x^2} + {y^2}} \right),{\varepsilon _y} = k{y^2},{\gamma _{xy}} = 2kxy$(${k \ne 0}$) C: ${\varepsilon _x} = 0,{\varepsilon _y} = 0,{\gamma _{xy}} = kxy$(${k \ne 0}$) D: ${\varepsilon _x} = ax{y^2},{\varepsilon _y} = b{x^2}y,{\gamma _{xy}} = cxy$($a \ne 0,b \ne 0,c \ne 0$)
- 下列微分方程中,( )是齐次方程。 A: \( xy' = y(\ln y - \ln x) \) B: \( xy' + {y \over x} - x = 0 \) C: \( y' + {y \over x} = {1 \over { { x^2}}} \) D: \( y - y' = 1 + xy' \)