Use polar coordinates to find the limit. [if (r, θ) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0 as (x, y) → (0, 0).] (if an answer does not exist, enter dne.) lim (x, y)→(0, 0) (x2 y2) ln(x2 y2)

Need ! give step by step solutions on how to solve number one \frac{9-2\sqrt{3} }{12+\sqrt{3} } number two x+4=\sqrt{13x-20} number three (domain and range) f(x)=2\sqrt[3]{x} +1

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. using the two given  measures, find the other four.