The solutions found in post #10 are correct but I am afraid their might be more that ht method I used there is missing. I hate using reasoning in math, that is why I dislike and mistrust the whole concept of proof. Trouble is, computation although more reliable can leave you hanging.
This will be the toughest baffler ever posed here.
Disclaimer: Do not try this problem and then drive or operate heavy machinery.
Okay, you see that side PQ is the square root of 3 and the equation of the ellipse is given below it.
The rules are rather extreme:
You may not use any CAS, that means Mathematica, Maxima, Wolfram Alpha, Maple, Matlab, Mupad, Octave, Pari, Yacas, Fricas, Magma.
You may not use any programming language, that means C, C++, Wolfram, Haskell, Basic, Pascal, Cobol, Fortran, Python or any other.
You may not use any mathematics that means calculus, group theory, algebra, trigonometry, geometry (Euclidean or any other), probability, any math theorem.
You can only use the tools of EM or you can try the force.
Okay, now for the question:
If we move P and Q along the circumference of that ellipse what is the sum of the largest area and the smallest area for triangle POQ? Of course the length of PQ must always remain constant at
A says) 2.
B says) That is not correct.
C says) 6.022 x 10^23
D says) 0
E says) I know the answer.
Since the limit of -x^2 as x approaches 0 is 0 and the limit of x^2 as x approaches 0 is 0 andstays between them, the limit of it as x approaches 0 is also 0.
Intuitively we can understand by the following drawing that Mathegocart provided:
If your function the green line always stays between the red and the blue line, then as the red and the blue line get closer together the green line gets sandwiched in between.