Question

\(\lim\limits_{x\rightarrow7}\dfrac{\sqrt[4]{x+9}-2}{x-7}\)

Answer 1

Mới biết qua về lim, làm thử một bài:

Ta có \(\dfrac{\sqrt[4]{x+9}-2}{x-7}=\dfrac{\sqrt[4]{x+9}-2}{\left(\sqrt[4]{x+9}-2\right)\left(\sqrt[4]{x+9}+2\right)\left(\sqrt{x+9}+4\right)}=\dfrac{1}{\left(\sqrt[4]{x+9}+2\right)\left(\sqrt{x+9}+4\right)}\).

Do đó \(\lim\limits_{x\rightarrow7}\dfrac{\sqrt[4]{x+9}-2}{x-7}=\lim\limits_{x\rightarrow7}\dfrac{1}{\left(\sqrt[4]{x+9}+2\right)\left(\sqrt{x+9}+4\right)}=\dfrac{1}{32}\).