Question

Find the limits. Write infty or -infty where appropriate. lim_{xrightarrow2^-}frac{x^2-3x+2}{x^3-2x^2}

Limits and continuity
ANSWERED
asked 2021-02-01
Find the limits. Write \(\infty\ or\ -\infty\) where appropriate.
\(\lim_{x\rightarrow2^-}\frac{x^2-3x+2}{x^3-2x^2}\)

Answers (1)

2021-02-02
To Determine:
Find the limits.
\(\lim_{x\rightarrow2^-}\frac{x^2-3x+2}{x^3-2x^2}\)
Explanation:
To find the limit, we will factorize the numerator and denominator.
\(\lim_{x\rightarrow2^-}\frac{(x-2)(x-1)}{x^2(x-2)}\)
\(\lim_{x\rightarrow2^-}\frac{(x-1)}{x^2}\)
find the limit now
\(\frac{(2-1)}{2^2}=\frac{1}{4}\)
\(=0.25\)
Answer: \(\lim_{x\rightarrow2^-}\frac{x^2-3x+2}{x^3-2x}=0.25\)
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