Complete 3 page APA formatted essay: Explain in your own word.The anti-derivatives of the function in this part are non-existent.The rule can be utilised in situations when a limit has been ascertaine

Complete 3 page APA formatted essay: Explain in your own word.

The anti-derivatives of the function in this part are non-existent.

The rule can be utilised in situations when a limit has been ascertained to be in existence. The rule is utilised in establishing functions of limits within a situation where the limit is presumed to exist, but the value remains unknown. The rule can be utilised in calculating limits within real numbers, negative and positive infinities(Krantz, 2004). Within these circumstances, the functional values are assumed to be differentiable. The rule simply applies to situation presenting finite or infinite derivatives.

The rule should be used in finding limits in cases presenting a single application. When two applications are utilised the limit values calculation provides the original value. Where more than two applications exist, an answer can never be gotten

The series works through providing approximations which are infinitely differentiable. The approximation method utilises partial sums in providing estimations to an entire unknown function of a series. It utilises the first terms of a Taylor series to solve problems regarding some restricted domains in advanced stages of a series.

Integration can be defined as a mathematical concept utilised in calculus and is an inverse to differentiation. Integration consists of the area which is normally bounded by a graph and the subsequent axis. An example of an integral value calculated through integration would be amount of water in an irregularly shaped swimming pool. Knowing the various dimensions of the swimming pool, the water becomes surrounded by the walls, hence becoming the integral.

Integration solves problems relating to area of irregularly shaped forms. It solves these problems through utilisation of regular shapes like squares, and then effectively converting the irregular shape to a regular shape.

c) Give an example of were optimization might be used in the