1. Tìm lim tan(2x).tan[(pi/4) – x] x–>pi/4 2. Tìm lim x^2 [căn({x+2} / x)] – [căn 3({x+3} / x)] x–>

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1. $1)\displaystyle\lim_{x \to \tfrac{\pi}{4}} \tan(2x).\tan\left(\dfrac{\pi}{4}-x\right)\\ x \to \dfrac{\pi}{4} \Rightarrow \tan(2x) \to +\infty;\tan\left(\dfrac{\pi}{4}-x\right) \to 0\\ \Rightarrow \displaystyle\lim_{x \to \tfrac{\pi}{4}} \tan(2x).\tan\left(\dfrac{\pi}{4}-x\right)=0\\ 2)\displaystyle\lim_{x \to +\infty} x^2\sqrt{\dfrac{x+2}{x}}-\sqrt[3]{\dfrac{x+3}{x}}\\ =\displaystyle\lim_{x \to +\infty} x^2\sqrt{\dfrac{1+\dfrac{2}{x}}{1}}-\sqrt[3]{\dfrac{1+\dfrac{3}{x}}{1}}\\ =\displaystyle\lim_{x \to +\infty} x^2-1\\ =+\infty$

    

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