evaluate the limit:

Question

lim cos(x + pi/2)/x
x->0

Answer 1

cos(x+pi/2)
= cosx cos pi/2 - sinx sin pi/2
= 0 - sinx
= -sinx

so
limit cos(x+pi/2)/x as x----> o
= lim -sinx/x , x ---> 0
= -1

using the fact that lim sinx/x = 1