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Therefore 0 <= exp <=x^2*sqrt(2). LHS obviously const RHS obviously -> 0 as x -> 0 Hence by squeezing principle (inequalities on both sides but going to same thing as limits are taken) the middle thing is that limit as well ie 0.

Paper: No. There are a few intervals which satisfy criterium defining [c,d] etc (eg just by making d larger)... but suppose you have two of these intervals (say [3,5] and [2,6] - too late to algebra this rigorously but I think this is just to satisfy you anyway.. :-) ) Then the max M_2 of...

Is this an assignment question? If not I can put up the soln tomorrow..

Complexity a good question doth not necessarily make...

Well, obviously spherical geometry you can use for measuring distances on earth. Theoretically, on unit sphere, if you have triangle with angles a,b,c Then area(triangle)=a+b+c-Pi And the negative of the expression is the area in hyperbolic geometry.

Sub in the 3 possible values of z. basically, if z= one of 1,w,w^2 and we call the second poly P(z) then one of P(1), P(w), P(w^2) is equal to zero ie P(1)P(w)P(w^2)=0. Sub in P for answer. This is funny... first answer for ages, and after I did a polynomials lecture this arvo as well.. :-)

you can't get most things half right :-P

yes. it doesn't have much to do with maths though.

And please post future ones in the extracurricular part of the forum. This clearly doesn't belong here

sigh... mouse, you know that 1) this is probably an assignment q which you should do yourself 2) If it isn't, try to do it first, and don't just copy and paste/type it in and expect an answer 3) you'll be screwed come exam time if you don't understand it... Anyway, just trying to help in...

Cool. Now do the rest :-P

yes. But I can't afford one... and talk to write.. sigh

Affinity is a good chess player. And, archman, I will see you soon :-P

Bachelor of Medicine (Math.)??

btw, you spell it "weird"... :-) If in doubt just check your weird short bow of evisceration.

dodgy defns... I know all about it... lol

Sightreading is a matter of forcing yourself to learn chordy pieces (start easy) and just playing lots of stuff you don't know.. btw, sight-transposition on organ is killer... *shudders* thankfully, haven't had to do that for ages. Anyway, back to the point... if you want to learn to...

Available for 1081 help online if needed. PM (nothing requiring me to type lots and lots preferably... just problems you can't do)

Famous unsolved problem...

eg spherical geometry... On a unit sphere, the angle being "what you'd expect", the sum of the angles minus 2Pi (in radians) equals the area of said triangle.