Describe the procedure for finding critical points of a function in two independent variables

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.] ${\displaystyle \underset{(x,y)\to (0,0)}{lim}\frac{x^2-y^2}{\sqrt{x^2+y^2}}}$

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?

Imagine that there is a correlation of r = 0.65 between variable X and variable Y. Based on the correlation between these two variables (and only these two variables), what is a person's predicted value on variable Y, when his X value on variable X is a z score of 1.5? Please provide your answer as a z score with a minimum of three decimal places.

a) Find the functions

What tis the complete domain D and range R of the following multivariable functions:
${\displaystyle w=2\sin xy}$

Let ${\displaystyle f\left(x\right)=5\cdot 2^x}$
a. Write an equation for p, the parent function of f.
b. Give the equation for an asymptote of both p and f.

For a marketing analysis,you want to ask 125 people how they
like the colours red,green and blue.After your questions,your
questions,you discover that.
55 people like red.
60 people like blue.
50 people like green.