Write formulas for the indicated partial derivatives for the multivariable function.g(k, m) = k^4m^5 − 3kma)g_kb)g_mc)g_m|_(k=2)

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
${\displaystyle P\left(x\right)=-12x^2+2136x-41000}$
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?

Use polar coordinates to find the limit. [Hint: Let ${\displaystyle x=r\cos \text{and}y=r\sin }$ , and note that (x, y) (0, 0) implies r 0.] ${\displaystyle \underset{(x,y)\to (0,0)}{lim}\frac{x^2-y^2}{\sqrt{x^2+y^2}}}$

If E(t,x,y,z) and B(t,x,y,z)represent the electric and magnetic fields at point (x,y,z) at time t, a basic principle of electromagnetic theory says that ${\displaystyle \mathrm{\nabla }\times E=\frac{-\partial B}{\partial t}}$. In this expression ${\displaystyle \mathrm{\nabla }\times E}$ is computed with t held fixed and ${\displaystyle \frac{\partial B}{\partial t}}$ is calculated with (x,y,z) fixed.
Use Stokes

Simplifying a rational expression with two variables.
${\displaystyle \frac{x^2+xy-2y^2}{x^2+3xy+2y^2}}$

Evaluate ${\displaystyle {\int }_C{x}^2{y}^{2}dx+4x{y}^{3}dy}$ where C is the triangle with vertices(0,0),(1,3), and (0,3).
(a)Use the Greens

Contract analysis. A contractor's financial outlay X and labor force Y are random variables with bivariate pdf given by: ${\displaystyle f_{X,Y}(x,y)=kxy}$ for ${\displaystyle 10,000<x<100,000}$ and ${\displaystyle 10<y<20}$ and ${\displaystyle =0}$, elsewhere. (a) Evaluate constant k.
(b) Detemine the marginal pdf of X and Y.

Solve the polynomial inequality
${\displaystyle x^2-2x+1>0}$
and graph the solution set on a real number line. Express the solution set in interval notation.