Can someone check my work for the following and fix accordingly?
Evaluate the following limits.
1. lim [1-cos^(2) x]/x^2
x->0
2. lim [1-cos2x]/x^2
x->0
3. lim cotx/(pi/2 - x)
x->0
my work:
1. lim (sin^(2)x)/x^2
x->0
i'm stuck here ..
2. lim [sin^2 (x) + cos^2 (x) - cos^ 2(x) + sin^2 (x)]/ x^2
x->0
= lim [2sin^(2) x]x^2
x->0
i'm not sure what step to take next
3. lim [cos (pi/2 - x)]/ [sin (pi/2 -x)]
(pi/2 - x) -> 0
stuck here too..