Question

stie careva cat este?​

Answer 1

$l =\lim\limits_{x\to \infty}(2\sqrt x - \ln x)\\ \\\\ \sqrt x = t \Rightarrow x = t^2\Rightarrow t\to \infty \\ \\\\ l = \lim\limits_{t\to \infty }(2t-\ln t^2) = \lim\limits_{t\to \infty}(2t-2\ln t) = 2\lim\limits_{t\to \infty}(\ln e^t-\ln t) \\ \\ l=2 \lim\limits_{t\to \infty}\ln \dfrac{e^t}{t} = 2\ln\Big(\lim\limits_{t\to \infty}\dfrac{e^t}{t}\Big) \overset{\frac{\infty}{\infty}}{=}2\ln \Big(\lim\limits_{t\to \infty}\dfrac{e^t}{1}\Big) = \\ \\ = 2\ln \infty = \boxed{\infty}$