These type of questions aren't even in the four unit syllabus are they? I mean I have no idea how to even to begin attempting this problem.Polys/Complex. Difficulty 3/5.
Well, they only aren't in the syllabus in the sense that some of them are harder than any question the bos would set in an actual HSC paper.These type of questions aren't even in the four unit syllabus are they? I mean I have no idea how to even to begin attempting this problem.
Just checking, but is the answer p=2?Let f be a real-valued function defined on R. For which values of the real constant p does the inequality below imply that f is twice differentiable?
|f(x)-f(y)| =< C|x-y|^p for all x,y. C a constant.
Justify your answer with proof.
p=2 is not quite good enough to get second differentiability (consider f(x)=x^3/|x|, f(0)=0. this func is not twice diffble at 0, yet obeys the p=2 bound), (also, there is more than value of p that works).Just checking, but is the answer p=2?
Hint: Use the fundamental theorem of calculus: a polynomial of degree n, has n roots. Let set A be all the roots and let set B be A-1. From that you can see that B^2 is always a root. If B is a complex number and its modulus is bigger than one, you get an infinite number of solutions; this can not happen because you only should have n roots. If the modulus of that complex number is between 0 and 1 same thing happens therefore that the modulus has got to be 0 or 1 and continue this logic ...These type of questions aren't even in the four unit syllabus are they? I mean I have no idea how to even to begin attempting this problem.
The red marker has me stumped. But I think I can do it if it is green.A (2 dimensional) ball with radius 'r' has a fixed red marker on it. It is rolled along the flat ground and the red marker leaves a trail in the air.
If the ball was initially above the origin with the marker being at the origin. Find the Cartesian equation describing the path of the marker.
Perhaps the assumption should instead be:
Yep thanks for the correction.Perhaps the assumption should instead be:
"Two opposite sides are equal and parallel."