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sqrt(x) has vertical tangent x=0 log(x)... hmm... this one.. is a bit strange hahaha... I dont think this has an endpoint... (with my definition of endpoint anyway)

haha thanks ngai ur very good at showing other people's mistakes, hey? anyway I'll give the situation where critical point exists (taken off my ext2 notes): -> if the tangent is vertical -> at any point of discontinuity in the original function -> at an endpoint of a finite domain (a...

I don't think anyone has corrected this.. but, absolute value is continuous! continuous at x=a is when the following 3 values exist and are equal: (1) the value of f(a) (2) the limit of the value of f(x) as x->a^- (3) the limit of the value of f(x) as x->a⁺ ---- EDIT: or...

there are a few more.. most are from HSC (although this one may not be.. and I dont think it is becoz it doesnt say it is) basically its to show how hard the Q's should be, and to limit the depth of the question asked. as far as I know, they tend to be the upper-end questions (i.e. they dont...

no way! I want 6 to be greater than 9!! It's a breakthough in maths history!!!!

IMO (in my opinion, or otherwise) participants of this forum should get it easily ;)

from ur statement to be proven, yes. thats why ur question is wrong :p

I think it shud be 7/13, because for the second student to be from Senior, the first must be from Junior. P(first from Junior) = 700/1300 = 7/13

Note: answer may not be correct.. (i) 700/1300 * 200/600 + 600/1300 * 400/700 (ii) 1/2 * (400/700 + 400/699) (I'm taking average of the two cases.. not sure if it can be done..) waiting for authoritative answer... EDIT: part (ii) is incorrect, keep scrolling.....

true true... radioactive algebraic decay, it is. half life of 30 minutes. now it seems to have disappeared almost completely... approaches zero.

I tried doing the 2003 HSC (at home.. under somewhat relaxed condition) and I didnt go too well :( went seriously over time haha its a good past paper btw ;)

I did, hehehe..

so u mean mine isnt easy to follow??

no, its called a distortion of algerba and occurs naturally after repeated algebraic manipulation ;)

so we have three methods? :confused: the one by withoutaface seems to be most elegant ; ) whoops.. its edited <== hidden treasure

?? why? =p(tm) EDIT: well now I know why =p (tm) =p(tm) is owned by CrashOveride or so he claimed.. :p let's quote CM_Tutor: hehehe.. ;)

here is the curve I give y=x for comparison. note: its not a sine curve along y=x.. its a kind of sine curve... the crests & troughs are not in the middle of the U-sphaped thing. But yea u need to differentiate to find stat pt... I cant think of any other approach.

that is NOT a parabola!! look closely.. the bottom end is a bit steep / looks like straight line. parabolas are all "similar", only enlarged by some constant factor. the red one in the pic is mr parabola the blue one is mr non-parabola ok?(tm) (tm) ok?(tm) is a trademark of its...

yes yes... I'm so happy.. maths is indeed interesting now I can start arguing with my teacher

its NOT a parabola. by definition, a parabola is... the locus of point P(x,y) such that the following 2 distances are equal: 1. the perpendicular distance to a fixed line (directrix) from P 2. the distance to a fixed point (focus) from P this creates a shape which is distinct from that...