Final answer:
The limit of the given expression is 0.
Step-by-step explanation:
The given expression limh→0cos(3π2 h)−cos(3π2)h involves the limit as h approaches 0. We can use the trigonometric identity cos(A - B) = cosAcosB + sinAsinB to simplify the expression. Applying this identity, we have:
limh→0 cos(3π/2 - 3π/2 h) - cos(3π/2)h = cos(3π/2)cos(3π/2 h) + sin(3π/2)sin(3π/2 h) - cos(3π/2)h
Since cos(3π/2) = 0 and sin(3π/2) = -1, the expression becomes:
limh→0 0*cos(3π/2 h) + (-1)*sin(3π/2 h) - 0*h
limh→0 -sin(3π/2 h) = -sin(0) = 0