Solve lim_{xto1}frac{(x^{4}-4)}{(x^{2}-3x+2)}

Solve lim_{xto1}frac{(x^{4}-4)}{(x^{2}-3x+2)}

Question
Limits and continuity
asked 2021-02-22
Solve \(\lim_{x\to1}\frac{(x^{4}-4)}{(x^{2}-3x+2)}

Answers (1)

2021-02-23
If \(\lim_{x\to a-}f(x)\neq \lim_{x\to a+}f(x)\) then the limit does not exist
\(\implies \lim_{x\to 1+}\frac{(x^{4}-4)}{(x^{2}-3x+2)}= \lim_{x\to 1+}((x^{4}-4)(x^{2}-3x+2)^{1})\)
\(= \lim_{x\to 1+}(x^{4}-4)\times\lim_{x\to 1+}((x^{2}-3x+2)^{-1})\)
\(=(-3)(-\infty)\)
\(=\infty\)
\(\implies \lim_{x\to 1-}\frac{(x^{4}-4)}{(x^{2}-3x+2)}= \lim_{x\to 1-}((x^{4}-4)(x^{2}-3x+2)^1)\) \(= \lim_{x\to 1-}(x^{4}-4)\times \lim_{x\to 1-}((x^{2}-3x+2)^{-1})\) Conclution: the \limit is diverges
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