A: $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) - \frac{{\partial T}}{{\partial {q_k}}} = 0$
B: $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) - \frac{{\partial T}}{{\partial {q_k}}} = {Q_k}$
C: $\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) + \frac{{\partial T}}{{\partial {q_k}}} = {Q_k}$
D: 以上都不对
举一反三
- \[设z=z(x,y)是由方程f(cx-az,cy-bz)=0所确定的函数,则a\frac{\partial z}{\partial x}+b\frac{\partial z}{\partial y}=（）\] A: a B: b C: c D: 0
- \(已知二元函数f(x,y)=\sin{x^2y},则\frac{\partial f}{\partial x}(1,\pi)=(\,)\) A: \(\frac{\pi}{2}\) B: \(2\pi\) C: \(-2\pi\) D: \(-\frac{\pi}{2}\)
- 从$\sum\limits_{k = 1}^N {\left( {{Q_k} + Q_k^*} \right)\delta {q_k}} = 0$ 得到${Q_k} + Q_k^* = 0{\rm{ }}(k = 1,2...N)$，需要的条件是____。 A: 理想约束 B: 双面约束 C: 定常约束恒 D: 以上都不对
- 4.已知二元函数$z(x,y)$满足方程$\frac{{{\partial }^{2}}z}{\partial x\partial y}=x+y$，并且$z(x,0)=x,z(0,y)={{y}^{2}}$，则$z(x,y)=$（ ） A: $\frac{1}{2}({{x}^{2}}y-x{{y}^{2}})+{{y}^{2}}+x$ B: $\frac{1}{2}({{x}^{2}}{{y}^{2}}+xy)+{{y}^{2}}+x$ C: ${{x}^{2}}{{y}^{2}}+{{y}^{2}}+x$ D: $\frac{1}{2}({{x}^{2}}y+x{{y}^{2}})+{{y}^{2}}+x$
- \(已知u=e^{xyz},则\frac{\partial^3u}{\partial x\partial y\partial z}=(\,)\) A: \[(x^2y^2z^2+zyz+1)e^{xyz}\] B: \[(x^2yz^2+3zyz+1)e^{xyz}\] C: \[(x^2y^2z^2+3zyz+1)e^{xyz}\] D: \[(x^2y^2z^2+3zyz)e^{xyz}\]
内容
- 0
Dead space like ventilation refer to () A: decrease<br/>of partial alveolar ventilation B: increase<br/>of partial alveolar VA/Q C: increase<br/>of partial alveolar ventilation D: decrease<br/>of partial alveolar VA/Q E: increase<br/>of anatomic shunt
- 1
9. 已知函数$z=z(x,y)$由${{z}^{3}}-3xyz={{a}^{3}}$确定，则$\frac{{{\partial }^{2}}z}{\partial x\partial y}=$（ ） A: $\frac{z({{z}^{4}}-2xy{{z}^{2}}-{{x}^{2}}{{y}^{2}})}{{{({{z}^{2}}-xy)}^{3}}}$ B: $\frac{z({{z}^{4}}-2xy{{z}^{2}}-xy)}{{{({{z}^{2}}-xy)}^{2}}}$ C: $\frac{z({{z}^{3}}-2xyz-{{x}^{2}}{{y}^{2}})}{{{({{z}^{2}}-xy)}^{3}}}$ D: $\frac{z({{z}^{3}}-2xy{{z}^{2}}-{{x}^{2}}y)}{{{({{z}^{2}}-xy)}^{3}}}$
- 2
（2）在深度负反馈条件下，下图所示电路的电压放大倍数为_____。 A: $\left( 1+ \frac{R_4}{R_5}\right) \cdot \frac{{R_6}//{R_{\rm L}}}{R_1}$ B: $\left( 1+ \frac{R_4}{R_5} \right) \cdot \frac{R_6}{R_1}$ C: $\frac{{R_6}//{R_{\rm L}}}{R_1}$ D: $\frac{R_4}{R_5} \cdot \frac{{R_6}//{R_{\rm L}}}{R_1} $
- 3
（4）方向导数$\frac{\partial f(1,1)}{\partial \vec{v}}$的最大值和最小值分别为( ) A: $1\ -1$ B: $2,\ -2$ C: $\sqrt{2}$，$-\sqrt{2}$ D: $2\sqrt{2}$，$-2\sqrt{2}$
- 4
1.设${{J}_{k}}=\int_{{}}^{{}}{\frac{dx}{{{\left[ {{(x+a)}^{2}}+{{b}^{2}} \right]}^{k}}}}\quad (b\ne 0)$，则${{J}_{k}}$满足( )。 A: ${{J}_{k+1}}=\frac{1}{2k{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}-(2k-1){{J}_{k}} \right],\quad (k\ge 2)$ B: ${{J}_{k+1}}=\frac{1}{2k{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k-1){{J}_{k}} \right],\quad (k\ge 2)$ C: ${{J}_{k+1}}=\frac{1}{2{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k+1){{J}_{k}} \right],\quad (k\ge 2)$ D: ${{J}_{k+1}}=\frac{1}{2{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k-1){{J}_{k}} \right],\quad (k\ge 2)$