Question

Calcule os seguintes limites
b) lim ln(5x+x^2)-ln5/x^2

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Answer 1

    $\lim_{x \to \infty} [\;ln(5x+x^2)-ln\:\frac{5}{x^2}\;]=$

$= \lim_{x \to \infty} \;ln(5x+x^2)-\lim_{x \to \infty} \;ln\:\frac{5}{x^2}\;=$

$= ln(5\times (+\infty)+(+\infty)^2)-ln\:\frac{5}{(+\infty)^2}=$

$=ln(+\infty+(+\infty))-ln\:\frac{5}{+\infty}=$

$=ln(+\infty)-ln(0^+)=$

$=+\infty-(-\infty)=$

$=+\infty+\infty=$

$=+\infty$