Question

limita x tinde spre infini x+3/x*-4. cine ma poate ajuta???
daca se poate detaliat. mersi

Answer 1

$\boxed{1} \quad \underset{x\rightarrow \infty}{lim} \dfrac{x+3}{x^{2}{-4}} = 0\\ \\ (polinom de grad mic pe polinom de grad mai mare, deja putem spune \\ ca limita este 0)$

$\boxed{2} \quad \underset{x\rightarrow \infty}{lim} \dfrac{x+3}{x^{2}{-4}} = \underset{x\rightarrow \infty}{lim} \dfrac{x\cdot\Big(1+ \dfrac{3}{x}\Big) }{x^{2}\cdot\Big(1{-\dfrac{4}{x^2}\Big) }} = \underset{x\rightarrow \infty}{lim} \dfrac{1\cdot\Big(1+ \dfrac{3}{x}\Big) }{x\cdot\Big(1{-\dfrac{4}{x^2}\Big) }} =$
$= \dfrac{1\cdot\Big(1+ \dfrac{3}{\infty}\Big) }{\infty\cdot\Big(1{-\dfrac{4}{\infty}\Big) }} = \dfrac{1\cdot\Big(1+ 0\Big) }{\infty\cdot\Big({1-0\Big) }} = \dfrac{1}{\infty} = 0$