(c) Find an algebraic expression for this force using a limiting case where d→ 0. (d) Find a more accurate algebraic approximation for this force by using a Taylor expansion.

This is a two-part question. A conservative force field is given by F = 6 sin (3x) i + 4yj. (a) Calculate the work done by the force field F along the path from (0,0) to (π,1). Enter the exact value of your answer in the box below. sqrt(8) (b) Enter the value of Number fo² F. dr in the box below, where C is a closed path.

The position r(t) of an object moving in 1-D on the r – aris in an inverse-square force field (such as an electromagnetic field) is given by Assume that the initial position of the object is known, i.e. r = xo > 0. Show that the velocity of the body at time t is given by v?(t) = 2k2