Đáp án:
`-6`
Giải thích các bước giải:
`\lim_{x \to 2} \frac{2-x}{\sqrt[x+7]-3}`
`=\lim_{x \to 2} \frac{(2-x)(\sqrt[x+7]+3)}{(\sqrt[x+7]-3)(\sqrt[x+7]+3)}`
`=\lim_{x \to 2} \frac{(2-x)(\sqrt[x+7]+3)}{x+7-9}`
`=\lim_{x \to 2} \frac{(2-x)(\sqrt[x+7]+3)}{x-2}`
`=\lim_{x \to 2} \frac{-(x-2)(\sqrt[x+7]+3)}{x-2}`
`=\lim_{x \to 2} -(\sqrt[x+7]+3)`
`= -(\sqrt[2+7]+3)`
`= -6`
Vậy `\lim_{x \to 2} \frac{2-x}{\sqrt[x+7]-3}=-6`
