The provided image contains mathematical problems. Let me analyze and solve the problems systematically. If you would like me to focus on specific questions, let me know. I’ll start with Question 1.

1. Given $z = x^2 + xy - y^2 - x - 2y$; find $D(1, -1)$:

1. Compute the partial derivatives $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$.

   • $\frac{\partial z}{\partial x} = 2x + y - 1$
   • $\frac{\partial z}{\partial y} = x - 2y - 2$

2. Evaluate the derivatives at $D(1, -1)$:

   • $\frac{\partial z}{\partial x} \big|_{(1, -1)} = 2(1) + (-1) - 1 = 0$
   • $\frac{\partial z}{\partial y} \big|_{(1, -1)} = (1) - 2(-1) - 2 = 1$

Would you like me to continue solving all the questions step by step, or focus on specific ones? Let me know! Below are possible next steps:

1. Would you like the full solution for Question 2 (integration)?
2. Should I solve Question 3 (more integrals)?
3. Would you like explanations for solving the differential equations in Question 5 or 6?
4. Do you need help with the system of equations in Question 4?
5. Shall I calculate the integral in Question 8?

Tip: When solving differential equations, always verify the general solution satisfies the initial conditions (if given).