let g be the function given by g(x ) = limh → 0 (cos x+h− cosx )/h what is the instantaneous rate of change of g with respect to x at x = x/3

Answer 1

The given limit is the definition of the derivative of cosx.

g(x) = (cosx)' = -sinx

instantaneous rate of change of g(x) = g' (x) = -cosx

Assuming that you mean x = π/3, g'(π/3) = -cos(π/3) = -1/2