The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Applications Of Functions

Functions arise in a great variety of situations. Here are some examples.


  • πr2 = area of a circle of radius r
  • 4πr2 = surface area of a sphere of radius r
  • 4/3πr3 = volume of a sphere of radius
  • r sin θ = the sine of the angle θ


  • s(t) = distance a particle travels from time 0 to t
  • v(t) = velocity of a particle at time t
  • a(t) = acceleration of a particle at time t
  • p(y) = water pressure at depth y below the surface
  • C = 5/9(F - 32) = Celsius temperature as a function of Fahrenheit temperature


  • f(t) = population at time t
  • p(t) = price of a commodity at time t
  • c(x) = cost of x items of a commodity
  • D(p) = demand for a commodity at price p, i.e., the amount which can be sold at price p

Functions of two or more variables can be dealt with in a similar way. Here is the precise definition of a function of two variables.

Last Update: 2006-11-14