[tex]\begin{gathered} \lim_{x\to-\infty}x^3(x+3)(-5x+1)=\lim_{x\to-\infty}x^3\lim_{x\to-\infty}(x+3)\lim_{x\to-\infty}(-5x+1) \\ \lim_{x\to-\infty}x^3=-\infty \\ \lim_{x\to-\infty}(x+3)=-\infty \\ \lim_{x\to-\infty}(-5x+1)=\infty \\ \therefore\lim_{x\to-\infty}f(x)=\infty \\ \lim_{x\to\infty}x^3(x+3)(-5x+1)=\lim_{x\to\infty}x^3\lim_{x\to\infty}(x+3)\lim_{x\to\infty}(-5x+1) \\ \lim_{x\to\infty}x^3=\infty \\ \lim_{x\to\infty}(x+3)=\infty \\ \lim_{x\to\infty}(-5x+1)=-\infty \\ \therefore\lim_{x\to\infty}f(x)=-\infty \end{gathered}[/tex]
Answer: Third option
