  Centrale des maths - centraledesmaths.uregina.ca  Dilemmes & doutes    « D & D »    Sujet: fallacy   nouvelle recherche

4 articles trouvés pour ce sujet.    Page1/1            The derivative of y=x^x 2010-04-09 David pose la question :So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did: It is commonly know that df(x)/dx of a function is also the limit as h->0 of f(x+h)-f(x)/h. To do this for x^x you have to start with lim h->0 ((x+h)^(x+h)-x^x)/h. The binomial theorem then shows us that this is equal to lim h->0 (x^(x+h)+(x+h)x^(x+h-1)h+...-x^x)/h This is also equal to lim a->0 lim h->0 (x^(x+a)+(x+h)x^(x+h-1)h...-x^x)/h. Evaluating for a=0 you get lim h->0 (x^x+(x+h)x^(x+h-1)h...x^x)/h Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get: lim h->0 (x+h)x^(x+h-1)... which when evaluated for h=0 gives us: x(x^(x-1)). This statement is also equal to x^x. This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that.Robert Dawson lui répond.     A riddle 2003-11-19 Sarah pose la question :Ok, our teacher gave us this riddle, and I cannot for the life of me figure it out. He said that there are three problems with the following proof:Penny Nom lui répond.     A proof that 1=2 2000-09-19 sporky pose la question :Why does the proof for 1=2 not work? x = 1 x2 = 1 x = x2 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ??? please tell me where the false logic is. Walter Whiteley lui répond.     2 = 1 2000-02-16 Chuck Kennedy pose la question :Question: Assume a=b Multiply both sides by a, a2=ab Subtract b2, a2-b2=ab-b2 Factor (a-b)(a+b)=b(a-b) Cancel like factors a+b=b Substitue b for a b+b=b Then 2b=b Therefore 2=1 Question; Were is the mistake?Claude Tardif lui répond.      Page1/1    Centrale des maths reçoit une aide financière de l’Université de Regina et de The Pacific Institute for the Mathematical Sciences.    Qui sommes-nous :: carte du site :: our english site