Fill in the blanks to complete each of the following theoremstatements: The derivative of a vector function r(t) is given by r'(t) =limh→0__________________. The Chain Rule for Vector-Valued Functions: Let t = f (τ) bea differentiable real-valued function of τ, and let r(t) bea differentiable vector function with either two or threecomponents such that f (τ ) is in the domain of r for everyvalue of τ on some interval I. Then dr/dτ =_______________ . Let C be the graph of a twice-differentiable vector functionr(t) defined on an interval I and with unit tangent vector T(t). Then the curvature κ of C at a point on the curve is given by κ = ||__________|| / ||__________|| and κ = ||_____x______||/||_________||3 Let y = f (x) be a twice-differentiable function. Then thecurvature of the graph of f is given by κ =|         | / (        )3/2 Let C be the graph of a vector function r(t) = ⟨x(t), y(t)⟩ inthe xy-plane, where x(t) and y(t) are twice-differentiablefunctions of t such that x'(t) and y'(t) are not simultaneouslyzero. Then the curvature κ of C at a point on the curve is given by κ =|         | / (        )3/2.