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LolWolf Group TitleBest ResponseYou've already chosen the best response.0
To make it look nicer, a proof of: \[\sin (ax^2)\sim ax^2, x \to 0\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
same as \[\lim_{x\to 0}\frac{\sin(ax^2)}{ax^2}=1\] many methods but if you know that \[\lim_{x\to 0}\frac{\sin(x)}{x}=1\] then this is identical
 one year ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.0
Well, a proof without l'Hospitals rule, I mean, I can prove the rule and I can prove the latter case trigonometrically and using IVT... but I want a nice, semirigorous algebraic proof of this... because I have no clue, how I would derive the former from the latter case.
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
algebra will not do it because you have a trig function
 one year ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.0
Sorry, let me say it more precisely, a proof that does not require analysis, differentiation, or use of other, largely nontrivial methods, other than a) Geometrical arguments, b) Manipulation of the latter case, stated three posts ago. I hope I was more precise, now.
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
dw:1346562207346:dw
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
sinx*cosx/2<sinx/2<tanx/2
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
areas of triangles
 one year ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.0
Yes, but what about sin(ax^2)?
 one year ago
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