(i)

(ii)

Anish Buchanan
2021-01-06
Answered

Let $z(x,y)={e}^{3xy},x(p,q)=\frac{p}{q}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y(p,q)=\frac{q}{p}$ are functions. Use multivariable chain rule of partial derivatives to find

(i)$\frac{\partial z}{\partial p}$

(ii)$\frac{\partial z}{\partial q}$ .

(i)

(ii)

You can still ask an expert for help

SoosteethicU

Answered 2021-01-07
Author has **102** answers

(i)

Using these values equation (1) becomes:

(ii)

asked 2021-09-08

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.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2021-09-30

Requires Uploaded Supporting Analysis:
Differentiate.
$y={(3{x}^{2}+5x+1)}^{\frac{3}{2}}$

asked 2021-01-19

Using the Divergence Theorem, evaluate $\int {\int}_{S}F.NdS$ , where $F(x,y,z)=({z}^{3}i-{x}^{3}j+{y}^{3}k)$ and S is the sphere $x}^{2}+{y}^{2}+{z}^{2}={a}^{2$ , with outward unit normal vector N.

asked 2022-07-04

What is the Proximal Operator ($\mathrm{Prox}$) of the Pseudo ${L}_{0}$ Norm?

Namely:

${\mathrm{Prox}}_{\lambda {\Vert \cdot \Vert}_{0}}\left(\mathit{y}\right)=\mathrm{arg}\underset{\mathit{x}}{min}\frac{1}{2}{\Vert \mathit{x}-\mathit{y}\Vert}_{2}^{2}+\lambda {\Vert \mathit{x}\Vert}_{0}$

Where ${\Vert \mathit{x}\Vert}_{0}=\mathrm{n}\mathrm{n}\mathrm{z}(x)$, namely teh number of non zeros elements in the vector $\mathit{x}$.

Namely:

${\mathrm{Prox}}_{\lambda {\Vert \cdot \Vert}_{0}}\left(\mathit{y}\right)=\mathrm{arg}\underset{\mathit{x}}{min}\frac{1}{2}{\Vert \mathit{x}-\mathit{y}\Vert}_{2}^{2}+\lambda {\Vert \mathit{x}\Vert}_{0}$

Where ${\Vert \mathit{x}\Vert}_{0}=\mathrm{n}\mathrm{n}\mathrm{z}(x)$, namely teh number of non zeros elements in the vector $\mathit{x}$.

asked 2021-11-15

The analysis of tooth shrinkage by

Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. In about how many years will human teeth be 90% of their present size?

Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. In about how many years will human teeth be 90% of their present size?

asked 2021-01-04

Suppose S is a region in the xy-plane with a boundary oriented counterclockwise. What is the normal to S? Explain why Stokes’ Theorem becomes the circulation form of Green’s Theorem.