Question

limita cand x tinde la infinit din (x+1/2x+3)^(x^2)

Answer 1

Răspuns:

⇆$\lim_{x \to \infty} (\frac{x+1}{2x+3}) ^x^{2}$

Adui si scazi 1  la    la    baza

lim(1-1+$(\frac{x+1}{2x+3} )^x^{2}$=

lim(1+$\frac{2x+1-2x-3}{2x+3} )^x^2$=

lim(1-$(\frac{2}{2x+3} )^x^2$ ridici   baza  concomitent la   puterea $\frac{-2}{2x+3} *\frac{2x+3}{-2} =1$

obtii[(1-$[(\frac{2}{2x+3} )^\frac{2x+3}{-2} ]^\frac{-2}{2x+3} ^x^2$

in  paranteza  dreapta   , la   limita   este   e⁻¹

e$-lim\frac{x^2}{2x+3}$=e^-∞=0

Explicație pas cu pas: