Hello can you provide a response to each part of the problem? Please provide all of the steps and explanations/math identities behind the steps for my understanding (because I am very new to calculus). This involves simple Vector Calculus/advanced math topics.

1. A formula for the curvature of the graph of a function in the xy-plane a. The graph y = f(x) in the xy-plane automatically has the parametrization x = x, y = f(x), and the vector formula r(x) = xi + f(x)j. Use this formula to show that if f is a twice-differentiable function of x, then If" (x)| K(X) = [1 + (f' (x ) ) 2 3/2 " Space Curves Find T, N, and k for the space curves in Exercises 9-16. 10. r(t) = (cost + t sin t)i + (sint - t cost)j + 3k Physical Applications 18. An object of mass m travels along the parabola y = x2 with a con- stant speed of 10 units / sec. What is the force on the object due to its acceleration at (0, 0)? at (21/2, 2)? Write your answers in terms of i and j. (Remember Newton's law, F = ma.)