**TI82** TxtView file generated by CalcText - Kouri¥–Mlogaryt–”ÿMaths logarythmex appartient a 0 exclu et tend => +8 ln 1 = 0 ln'x = 1/x ln(ab) = ln(a) + ln(b) ln(1/b) = -ln(b) ln(a/b) = ln(a) - ln(b) ln(a^n) = n ln(a) n appartient Z ln (raccine(a)) = 1/2 ln a lim ln x = -8 x->0 lim ln x = +8 x->+8 lim ln(x) / x =0 x->+8 lim xln(x) =0 x->0 lim ln(1+h)/h = 1 h->0 lim ln(x)/(x-1) = 1 x->1 DEM : ln(ab) = ln(a) + ln(b)? e(ln(a) + ln(b)) = e(ln(a)) + e(ln(b)) = ab e(ln(ab)) = ab --------------------------------------------------- ln(1/b) = -ln(b)? ln(1/b) + ln(b) =0 ln(b/b) =0 ln(1) =0 --------------------------------------------------- ln(a/b) = ln(a)-ln(b)? ln(a/b) = ln(a)+ln(1/b) ln(a/b) = ln(a)-ln(b) --------------------------------------------------- ln(x^n) = n ln(x) ==> hérédité Calcul : ln(x^(n+1)) = ln(x x^n) = ln (x^n) + ln (x) =(n+1) ln (x ) --------------------------------------------------- lim ln(x) = +8 x->+8 Soit A>0 il existe B tel que x>B ln(x)>A ln(x)>A <=> x > e^A B = e^A --------------------------------------------------- lim ln(x) = -8 ??? x->0+ Soit X = 1/x ( je sais pour le OMG ) ( tu risque pas de le trouver tout seul hein ? ) lnx = ln(1/X) = -ln X lim 1/x = +8 X -> 0+ lim -ln X = -8 X -> +8 lim ln(x) = -8 x->0+ -------------------------------------------------- lim ln(x)/x = 0 ??? x->+8 Soit X = ln(x) e^X = x ln(x) / x = X / e^X = 1/e^X/X lim ln(x) = +8 x->+8 lim 1/e^X/X = 0 X-> +8 car lim e^X/X = +8 quand x->+8 --------------------------------------------------- lim xln(x) = 0 ? x->0 Soit X = 1/x lim xln(x) = lim 1/X ln(1/X) = lim -ln(X) / X lim 1/x = +8 x->0+ lim -lnX/X = 0 x->+8ÿ<‹