To start, let's find the value of x as it gets closer to 0 from the positive side (we are working on the first example). To start, when x is 1, we have sin(2) - 2. This is approximately -1.965. Now, plugging in 2, we get (sin(4)-4)/8. This is -0.491. Now, we plug in 1/2 to get 8sin(1) - 8. This is approximately -7.86. Plugging in something like 1/1000, we will get -1965. Notice that there is no limit to it, so the answer is negative infinity, or DNE (IDK)
A regular polygon is equilateral (it has equal sides) and equiangular (it has equal angles). To find the area of a regular polygon, you use an apothem — a segment that joins the polygon's center to the midpoint of any side and that is perpendicular to that side (segment HM in the following figure is an apothem).
The equation

is a quadratic equation, with the quadratic term 6x^2, the linear term x, and the constant term -12.
Take the base-3 log, or simply equate the exponents.
2x+1 = x+5
Subtract x+1
x = 4