Question

va rog ajutor aici!!!!!!

Answer 1

a) Cercetăm existența asimptotei orizontale spre $+\infty$ la Gf de ecuație $y=l\in\mathbb{R}$.

$\displaystyle l=\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}\frac{x+1}{x+2}\overset{\frac{\infty}{\infty}}{=}1\in\mathbb{R}\Rightarrow y=1\text{ asimptot\u a orizontal\u a spre }+\infty.$

b) $\displaystyle f'(x)=\frac{(x+1)'(x+2)-(x+1)(x+2)'}{(x+2)^2}=\frac{x+2-x-1}{(x+2)^2}=\frac{1}{(x+1)^2}>0,\forall x\in(-2,\infty)\Rightarrow f \text{ strict cresc\u atoare.}$