Limita

MaTe1997 · Mesaj de **MaTe1997** » 27 Apr 2016, 11:07

limita cand x tinde la 0 din (x^n-(tg(x))^n)/x^n.
Am folosit remarcabila tg(x)/x si dupa am aplicat 1 data l'Hospital.Dar mie imi da limita 0,iar raspunsul corect este -n/3.
Multumesc frumos!!

Mesaj de DD » 27 Apr 2016, 13:02

(x^n-(tgx)^n)/x^(n+2)=[(x-tgX)/x^3].((x^(n-1)+x^(n-2).tgx+......+(tgx)^(n-1))/x^(n-1)=
lim(x-0)[(x-tgx).x^(3)][1+(tgx/x)+(tgx/x)^2+.....+(tgx/x)^(n-1))=lim(x->0)[n.[x-tgx]/x^3.=lim(x->0)[n(x-(x-x^3/3)/x^3]=-n/3

MaTe1997 · Mesaj de **MaTe1997** » 27 Apr 2016, 13:08

Multumesc frumos!!!Frumoasa rezolvare :)