lim x^3-3x-2/x^3-8 x->2. Created by rahatik05. algebra-ru

x^3-8 x->2...

rahatik05 @rahatik05

July 2022 1 3 Report

lim x^3-3x-2/x^3-8 x->2

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Dимасuk

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$\lim_{x \to 2} \dfrac{x^3 - 3x - 2}{x^3 - 8} = \lim_{x \to 2} \dfrac{x^3 + x^2 - x^2 - x - 2x - 2}{(x - 2)(x^2 + 2x + 4)} = \\ \\ 
= \lim_{x \to 2} \dfrac{x^2(x + 1) - x(x + 1) - 2(x + 1)}{(x^2 + 2x + 4)(x - 2)} = \\ \\ 
= \lim_{x \to 2} \dfrac{(x^2 - x - 2)(x + 1)}{(x - 2)(x^2 + 2x + 4)} = \\ \\ 
= \lim_{x \to 2} \dfrac{(x^2 + x - 2x - 2)(x + 1)}{(x - 2)(x^2 + 2x + 4)} = \\ \\ 
= \lim_{x \to 2} \dfrac{(x - 2)(x + 1)(x + 1)}{(x - 2)(x^2 + 2x + 4)} = \\ \\ 

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$= \lim_{x \to 2} \dfrac{(x + 1)^2 }{x^2 + 2x + 4} = \dfrac{(2 + 1)^2}{2^2 + 2^2 + 4} = \dfrac{9}{12} = \dfrac{3}{4}$

0 votes Thanks 1

rahatik05 я хз что ты написал но спс

Dимасuk обнови страницу, я скрин добавил

rahatik05 а если один х из х^3 на 2 поменять?

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celi i plan molnienosnoj vojny nachalnika gen shtabakratko

x^3-1 x->1...

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