1. ## Limits

Hey!

I'm not quite sure how to proceed in calculating this limit.
If you could look at it and give me some feedback I would appreciate it.

$\lim_{x \to +\infty} \frac{xln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1}$

$xln(e^x+e^{-x})$

= $x[ln(1+e^{-2x})+x]$

3. After using that, divide both numerator and denominator by $x^2$.

4. Thank you!

5. Here's a hand-waving argument, for large $x$

$
\frac{x \ln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1} \approx \frac{x \ln(e^x)}{x^2} = \frac{x^2}{x^2} = 1$

6. Originally Posted by mei
Hey!

I'm not quite sure how to proceed in calculating this limit.
If you could look at it and give me some feedback I would appreciate it.

$\lim_{x \to +\infty} \frac{xln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1}$

You can divide all three terms by $x^2$
and concentrate on ${\ln(e^x+e^{-x})\over x}$