Dear all,

I have two similar questions but I am not getting the idea how to solve it the second one, is the approach in first part is correct or not???

1. $\displaystyle \mathop {\lim }\limits_{x \to + \infty } {\left( {x + \frac{2}{x}} \right)^{3x}} $

Let $\displaystyle y = {\left( {x + \frac{2}{x}} \right)^{3x}}$, then

$\displaystyle \mathop {\lim }\limits_{x \to + \infty } y = \mathop {\lim }\limits_{x \to + \infty } {e^{\ln {{\left( {x + \frac{2}{x}} \right)}^{3x}}}}$

$\displaystyle = {e^{3x.\ln \left( {x + \frac{2}{x}} \right)}} = {e^{\mathop {\lim }\limits_{x \to + \infty } 3x.\ln \left( {x + \frac{2}{x}} \right)}}$

$\displaystyle = {e^{ + \infty . + \infty }} = + \infty $

Am I right here???

and Second one is

2. $\displaystyle \mathop {\lim }\limits_{x \to - \infty } {\left( {\left| x \right| + \frac{2}{x}} \right)^{3x}} $

how to proceed here???

Thanks in Advance.