АЛГЕБРА 10КЛАСС x-->x0 1) f(x)=2x-x^2 / x-2 ; x-->2 2) f(x)=x^3-27 / x-3 ; x-->3 3) f(x)=3x^2+2x-1 / x+1 ; x-->-1 4) f(x)=x^2-4 / x^4-16 ; x-->2. Created by Zholdasova2001. algebra-ru

x^4-16 ; x-->2...

Zholdasova2001 @Zholdasova2001

July 2022 1 11 Report

АЛГЕБРА 10КЛАСС x-->x0

1) f(x)=2x-x^2 / x-2 ; x-->2
2) f(x)=x^3-27 / x-3 ; x-->3
3) f(x)=3x^2+2x-1 / x+1 ; x-->-1
4) f(x)=x^2-4 / x^4-16 ; x-->2

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NNNLLL54

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$1)\; \; \lim\limits _{x \to 2}\frac{2x-x^2}{x-2}=\lim\limits _{x \to 2} \frac{x(2-x)}{-(2-x)} = \lim\limits _{x \to 2} (-x)=-2\\\\2)\; \; \lim\limits _{x \to 3} \frac{x^3-27}{x-3} = \lim\limits _{x \to 3}\frac{(x-3)(x^2+3x+9)}{x-3} = \lim\limits _{x \to 3}(x^2+3x+9)=27\\\\3)\; \; \lim\limits _{x \to -1}\frac{3x^2+2x-1}{x+1}=\lim\limits _{x \to -1}\frac{3(x+1)(x-\frac{1}{3})}{x+1} = \lim\limits _{x \to -1} (3x-1)=-4\\\\4)\; \; \lim\limits _{x \to 2}\frac{x^2-4}{x^4-16}=\lim\limits _{x \to 2}\frac{x^2-4}{(x^2-4)(x^2+4)}=\lim\limits _{x \to 2}\frac{1}{x^2+4}=\frac{1}{8}$

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