lim x->1. (x^4-x^3-2*x+2)/(x^2-3*x+2). Created by yahoo223. algebra-ru

(x^2-3*x+2)...

March 2022 1 7 Report

lim x->1. (x^4-x^3-2*x+2)/(x^2-3*x+2)

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sukonnikoffma $x^4-x^3-2x+2=x^3(x-1)-2(x-1)=(x-1)(x^3-2)
\\ x^2-3x+2=(x-1)(x-2)
\\ \lim_{x \to 1} \frac{x^4-x^3-2x+2}{x^2-3x+2}=\lim_{x \to 1} \frac{(x-1)(x^3-2) }{(x-1)(x-2)} =
\\ =\lim_{x \to 1} \frac{(x^3-2) }{(x-2)}= \frac{1^3-2}{1-2} =1$

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