Estimate the limit using L'Hopital's rule: 1. limit of x is going to infinity of xtan(1/x) Okay, I have no idea how to do #1, but i know the indetermiate form is infinity*0. 2. limit as x tends to 0+ of (lnx - ln sinx) For #2 the indeterminate form is infinity-infinity, so i took the derivative of the function and got: (1/x) - (cosx/sinx) which yields the same indeterminate form of infinity - infinity. So my question is, should i get both with a common denominator, or should i derive (1/x) - (cosx/sinx) again and plug 0 to see if it works? Any suggestions? For both 1 or 2?