Solve for x in the equation 5x+4=4-7n.

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

Explain how to find the limit of the identity function ${\displaystyle f\left(x\right)=x}$. Then express your written explanation using limit notation.

Solve for G.S. / P.S. for the following differential equations using separation of variables.
${\displaystyle 2{\sin }^{2}2tdx=\cos x(1+\cos 2x)dt}$

Describe in general terms how to solve a system in three variables.

(a)Show that for all complex numbers z and w
${\displaystyle {|z-w|}^2+{|z+w|}^2=2{\left|z\right|}^2+2{\left|w\right|}^2}$
(b) Let u,v be complex numbers such that ${\displaystyle \left|u\right|=\left|v\right|=1\text{and}|u-v|=2}$ Use part (a) to express u in terms of v.

${\displaystyle \frac{dy}{dx}=x\sqrt{1-y^2}}$ solve by seperation of variables.