Algebraic Operations on Limited Developments

This lecture covers algebraic operations on limited developments, including the derivative of the sum of two functions, the derivative of the product of two functions, and the consequences on the limited developments of sufficiently differentiable functions. The lecture also provides examples of calculating limited developments for functions like sin(x), cos(x), and exp(x) around a given point. The formula for the product of two functions' limited developments is derived and a theorem is stated regarding the limited development of the product of two functions. The examples demonstrate the application of these concepts in calculating the limited development of functions like sin(x) exp(x) and sin(x) + exp(x) around a specific point.