Find the limit lim_{xrightarrow-infty}frac{x^2-4x+8}{3x^3}

Find the limit lim_{xrightarrow-infty}frac{x^2-4x+8}{3x^3}

Question
Limits and continuity
asked 2021-02-25
Find the limit
\(\lim_{x\rightarrow-\infty}\frac{x^2-4x+8}{3x^3}\)

Answers (1)

2021-02-26
The given function is
\(\lim_{x\rightarrow-\infty}\frac{x^2-4x+8}{3x^3}\)
Solve the limit of the function
\(=\frac{1}{3}\lim_{x\rightarrow-\infty}\frac{x^2-4x+8}{x^3}\)
\(=\frac{1}{3}\lim_{x\rightarrow-\infty}(\frac{1}{x}-\frac{4}{x^2}+\frac{8}{x^3})\)
\(=\frac{1}{3}\lim_{x\rightarrow-\infty}[\lim_{x\rightarrow-\infty}(\frac{1}{x})-\lim_{x\rightarrow-\infty}(\frac{-4}{x^2})+\lim_{x\rightarrow-\infty}(\frac{8}{x^3})]\)
\(=\frac{1}{3}(0+0+0)\)
\(=0\)
Hence, the limit of the given function is 0.
0

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