Question

lim \(\dfrac{3x^2-x^5}{x^4+6x+5}\)

x-> +∞

 

Answer 1

\(\lim\limits_{x\rightarrow+\infty}\dfrac{3x^2-x^5}{x^4+6x+5}=\lim\limits_{x\rightarrow+\infty}\dfrac{x^5\left(-1+\dfrac{3}{x^3}\right)}{x^4\left(1+\dfrac{6}{x^3}+\dfrac{5}{x^4}\right)}\\ =\lim\limits_{x\rightarrow+\infty}\dfrac{x\left(-1+\dfrac{3}{x^3}\right)}{1+\dfrac{6}{x^3}+\dfrac{5}{x^4}}=-\infty\)

Answer 2

\( = \mathop {\lim }\limits_{x \to + \infty } \dfrac{{x\left( { - 1 + \dfrac{3}{{{x^3}}}} \right)}}{{1 + \dfrac{6}{{{x^3}}} + \dfrac{5}{{{x^4}}}}} = - \infty \)