I have got some HW problems based on limits and continuity...please help in solving those problems..
Q1) Find the limit of the following using L'Hospital rule....
a) lim x-> 0+ [sin(x) - x] / [e^x - 1]
b) lim x-> pi/2 [pi/2 - x] . tan(x)
Q2) Prove using the Mean value theorem: (x-1)/x < ln(x) < x-1, when x>1