Heaviside Function The Heaviside function is widely used in engineering applications.Hx 1,0, x 0x < 0HSketch the graph of the Heaviside function and the graphs of thefollowing functions by hand.(a) (b) (c)(d) (e) (f)OLIVER HEAVISIDE (18501925)Heaviside was a British mathematician and physicist who contributed to the field of applied mathematics, especially applications of mathematics to electrical engineering.The Heaviside function is a classic type of on-off function that has applications to electricityand computer science.

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