Did you try L'Hopitals rule for the first one. I got (3 - (3^.5)/6)

And for the second one sorry, Use the rules of logrithms to break it up. as I did below. (I will leave out the limit statement to make it easier to read.)

ln[(x+1)^((1+2x)/x)/(x^2+2x+1)]

ln[(x+1)^((1+2x)/x)] - ln(x^2+2x+1)

((1+2x)/x)ln(x+1) - ln(x^2+2x+1)

Then apply the limit statement to both parts of the problem sepetatly, and the second part ( the ln(x^2+2x+1)) will be solved. For the first part you will an awnser of 0/0, so apply L'Hopitals rule and you will get an awnser. I got 0 as my final awnser.