Question

lim x -∞ =(5+1/x+3/x^2)

Answer 1

Olá estudante, acompanha o raciocínio racional!

$\large {\boxed {\sf \lim_{x \to - \infty} \left ( 5+ \cfrac{1}{\cfrac{ x+3}{x^2}} \right ) }}$

Lembrando de:

$\huge {\boxed { \sf \lim _{x \to a} \left [f \left (x \right ) \pm g \left ( x \right) \right ]= \lim _{x \to a} f \left (x \right) \pm \lim _{x \to a} g \left( x \right) } }$

$\large {\boxed {\sf \lim _{x\to \: -\infty \:}\left(5\right)+\lim _{x\to \:-\infty \:} \left ( \cfrac{1}{ \cfrac {x+3}{x^2}} \right)}}$

$\huge {\boxed {\sf \lim_{x \to -\infty} (5) = 5 }}$

$\huge {\boxed {\sf \lim_{x \to - \infty} \left ( \cfrac{1}{\cfrac {x+3}{x^2}} \right ) = - \infty }}$

Contemos:

$\huge {\boxed {\sf c - \infty = - \infty }}$

Portanto (Resultado) :

$\huge { \boxed { \boxed {\boxed {\boxed { \sf - \infty}}}}}$

• Att. MatiasHP