Question

lim x-> infinit din x^a(x-ln(e^x+1))=0, pentru orice a apartine R.

Answer 1

[tex] \lim_{n \to \infty} x^a(x-ln(e^x+1))= inf(inf-inf)\\ \\ \lim_{n \to \infty} x^a(x(1- \frac{ln(e^x+1)}{x} ))= la-fractie-folosesti-l'Hospital \\ \\ \lim_{n \to \infty} x^{a+1} (1- \frac{e^x}{e^x+1} )= \\ \\ \lim_{n \to \infty} x^{a+1} ( \frac{1}{e^x+1} )= \\ \\ = \lim_{n \to \infty} \frac{ x^{a+1} }{e^x+1} =0[/tex]