Electric potential due to a charged cylinder. An infinitely long charged cylinder of radius R with its axis along the z-axis has an electric potential V = k ln 1R>r2, where r is the distance between a variable point P1x, y2 and the axis of the cylinder 1r2 = x2 + y22 and k is a physical constant. The electric field at a point 1x, y2 in the xy-plane is given by E = -_V, where _V is the two-dimensional gradient. Compute the electric field at a point 1x, y2 with r 7 R.

Calculus notes for week of 9/19/16 3.6 Derivatives as Rates of Change Velocity is measured as: V ave(t+∆t) or s(b) – s(a) ∆t b – a (Change in position over change in time.) S’’(t) = V’(t) = A(t) (From left to right: S=Position, V= Velocity, and A=Acceleration) Average and Marginal Cost Suppose C(x) gives the total cost to produce x units of a good cost. Sometimes, C(x) = FC + VC * x FC = Fixed cost which does not change with units produced. VC = Variable cost which is the cost to produce each unit. C(x) = Average cost. C’(x) = Marginal cost, which is approximately the extra cost to produce one more unit beyond x units. C’(x) = lim C(x+∆x) – C(x) ∆x>0 ∆x 3.7 Chain Rule How do we differentiate a composi