Thread: some help with indeterminate forms and L'hoepitals rule

1. some help with indeterminate forms and L'hoepitals rule

i got an exam on this stuff tomorrow, and im not completely comfortable with it.. heres a few that i tried on my own that i know i did wrong

limit as x approaches 0 from the right... sin x ln x
this one i guess goes to 0*(negative infinity).. thats obviously an indeterminate form, so we play around with it.. if you put 1/sin x, or csc x, in the denominator, it appears that the limit is undefined? but im pretty sure that is incorrect... why is it incorrect, and how do you actually do it?

lim as x approaches infinity.... x tan(1/x)
this one i got so confused with, so just briefly walk me through it if you can

lim as x approaches infinity... [sq.rt.(x^2 +x) - x]
this one goes to infinity - infinity.. another indeterminate... i used the conjugate technique to get infinity over infinity, so i can use loepitals rule... but i kept getting infinity over infinity (i believe)... how is this one done?

i am in need of big help for these so anything you can give me is much appreciated!!!

2. 1. look at sinx/{1/lnx} (0/0)

2. substitute t=1/x when x-->inf t-->0

3. ok so for the first one, i get sin x/ (1/ln x) .... which goes to 0/0... so after taking the derivatives, i get cos x/ x ...this goes to 1/0... is the limit undefined then? that is what i got initially when i brought csc x to the bottom, but as i said i thought undefined was wrong... any other advice or can you point out my mistake?