Find the solution of limit \lim_{(x,y)->0,0} sqrt((x^2+y^2)/(x^2+y^2)) by using the polar coordinates system

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces ${\displaystyle F_A}$ and ${\displaystyle F_B}$ exerted on the unit by the horizontal cables is parallel to the line L, and ${\displaystyle F_A=4200}$ N. Determine ${\displaystyle F_B}$? Determine the magnitude of ${\displaystyle F_A+F_B}$?

A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s a long its initial line of motion with an acceleration of 30.0 m/s/s. At this time, its engines fail and the rocket proceeds to move as a projectile. Find:
a) the maximum altitude reached by the rocket
b) its total time of flight
c) its horizontal range.

A 0.48 kg piece of wood floats in water but is found to sinkin alcohol (specific gravity= 0.79) in which it has an apparentmass 0.035 kg. What is the SG of the wood?

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors ${\displaystyle \hat{i}}$ and ${\displaystyle \hat{j}}$.
1. (Enter in box 1) $\frac{m}{s^2}\hat{i}+(\text{ Enter in box 2 })\frac{m}{s^2}\hat{j}$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) ${\displaystyle \frac{m}{s^2}\hat{i}+}$
5. ( Enter in box 5) ${\displaystyle \frac{m}{s^2}\hat{j}}$

Find the derivative.
$y(x)=x{\tanh }^{-1}(x)+\ln \hspace{0.17em}(\sqrt{1-x^2})$

Two 2.1cm diameter disks face each other, 2.9mm apart. They are charged to ${\displaystyle \pm 10nC}$.
a) what is the electric field strength between two disks?
b) a proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

A pump is used to transport water to a higher reservoir. If the water temperature is ${\displaystyle {20}^{\circ }C}$, determine the lowest pressure that can exist in the pump without cavitation.