## Abstract

Applications of the calculus depend on interpretations of the derivative, such as the slope of a graph, a velocity or an acceleration, marginal profit or cost or revenue, a rate of growth or of decay. For example, acceleration is the derivative of speed for a moving vehicle. Thus if the acceleration of an object is known to be constantly 7, then its speed *s*(*t*) as a function of time satisfies the equation *s*’(*t*) = 7. This is called a differential equation: it is an equation involving the derivative of a function. The solution to this equation is not a number; it is the function *s*(*t*) = 7*t* + *C*, where 7 is the constant acceleration and *C* is the number *s*(0), the value of the speed at the time coordinate 0. In general, in differential equations the unknowns do not stand for numbers but for functions, and the solutions are functions.

## Keywords

Taylor Series Series Solution Decimal Place Solution Function Remainder Term## Preview

Unable to display preview. Download preview PDF.