Question

Limx→+∞​ (x-(lnx)^2) =?​

Answer 1

`</p><p>\lim_(x\to\infty)(x-\ln(x)^2) \\</p><p>\lim_(x\to\infty)(x-2\ln(x)) \\</p><p>\lim_(x\to\infty)\Big(x\Big(1-(2\ln(x))/(x)\Big)\Big) \\</p><p>\lim_(x\to\infty)x\cdot\lim_(x\to\infty)\Big(1-(2\ln(x))/(x)\Big) \\</p><p>\infty\cdot\Big(\lim_(x\to\infty)(1)-\lim_(x\to\infty)\Big((2\ln(x))/(x)\Big)\Big) \\</p><p>\infty\cdot(1-2\lim_(x\to\infty)(1/x)) \\</p><p>\infty\cdot(1-0) \\</p><p>\infty\cdot1=\boxed{\infty}</p><p>`

Hope this helps.