Solve 8 Multivariable calculus problems

*Note: this aren't entry level multivariable calculus, please don't propose if you didn't saw the exercises* Algebraic procedure is needed for the solution of each problem attached in the documents. The problems require knowledge on the following matters: - Lagrange Multipliers - Area/Volume Integrals - Integrals over region - Region identification and transformation to other coordinate systems (polar, spherical, cylindrical) - Center of mass using integrals - Moment of inertia using integrals Guidelines: - Read the problems before you propose. Be sure that you are able to do the problems: - Generic proposals will be ignored. - Proposals that mention a different cost than the shown will also be ignored. - Please write the jacobian of a change from cartesian to polar coordinates to prove that you have read this. - Partial proposals are also allowed, For instance if you want to solve only 5 problems. Solution Guidelines: - Solutions can be handwritten, but must be clear and easy to understand - Region changes must be also written Read the problems here: [login to view URL] * Proposed milestones: X USD per exercise done*