(Original post by Jodin)
Hi, firstly, it's fine to write that lim x ->0 1/x = infinity, or rather it would be if it were true (consider a limit approaching from the negative numbers (1/-1, 1/-0.1, 1/-0.01, ...)
You're saved in this limit because you're restricted to x>0 'cause of the lnx.
Edit: The edits are because I massively misread your post, sorry about that.
Right, so is my answer to the first part of the question correct and sufficient ?