1. The user asked for questions on Calculus III, which typically involves multivariable calculus topics such as partial derivatives, multiple integrals, and vector calculus. 2. Since the user requested questions, here is a sample problem: "Find the partial derivatives of the function $f(x,y,z) = x^2y + yz^3 - e^{xz}$ with respect to $x$, $y$, and $z$." 3. To solve this, recall the definition of partial derivatives: the derivative of the function with respect to one variable while treating the other variables as constants. 4. Compute $\frac{\partial f}{\partial x}$: $$\frac{\partial}{\partial x}(x^2y + yz^3 - e^{xz}) = 2xy - \frac{\partial}{\partial x}(e^{xz}) + 0 = 2xy - ze^{xz}$$ 5. Compute $\frac{\partial f}{\partial y}$: $$\frac{\partial}{\partial y}(x^2y + yz^3 - e^{xz}) = x^2 + z^3 - 0 = x^2 + z^3$$ 6. Compute $\frac{\partial f}{\partial z}$: $$\frac{\partial}{\partial z}(x^2y + yz^3 - e^{xz}) = 0 + 3yz^2 - \frac{\partial}{\partial z}(e^{xz}) = 3yz^2 - xe^{xz}$$ 7. Therefore, the partial derivatives are: $$\frac{\partial f}{\partial x} = 2xy - ze^{xz}, \quad \frac{\partial f}{\partial y} = x^2 + z^3, \quad \frac{\partial f}{\partial z} = 3yz^2 - xe^{xz}$$ This completes the solution to the first Calculus III question.