Question

Find the limits. Write infty or -infty where appropriate. lim_{xrightarrow0^-}frac{x^2-3x+2}{x^3-4x}

Limits and continuity
ANSWERED
asked 2021-01-31
Find the limits. Write \(\infty\) or \(-\infty\) where appropriate. \(\lim_{x\rightarrow0^-}\frac{x^2-3x+2}{x^3-4x}\)

Answers (1)

2021-02-01

First let's write the limit
\(\lim_{x\rightarrow0^-}\frac{x^2-3x+2}{x^3-4x}\)
\(=\lim_{h\rightarrow0}\frac{x^2-3x+2}{x^3-4x}\)
\(=\lim_{h\rightarrow0}\frac{-h^2-3(-h)+2}{-h^3+4h}\)
\(=\lim_{h\rightarrow0}\frac{h^2+3g+2}{-h^3+4h}\)
Then, since h tends to 0, it must be fractional and less than 1
As \(h < 1\)
\(h^3\)
Hence, \(h^3<4h\)
\(4h-h^3>0\)
Hence, the denominator in the limit above approaches \(0^+\)
\(Limit=\frac{0+0+2}{0^+}=\infty\)
Result:\(\infty\)

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