Introduction to Calculus and Analysis II/1 pp 218-366 | Cite as

# Developments and Applications of the Differential Calculus

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## Abstract

Frequently in analytical geometry the equation of a curve is given not in the form y = f(x) but in the form F(x, y) = 0. A straight line may be represented in this way by the equation ax + by + c = 0, and an ellipse, by the equation x^{2}/a^{2} + y^{2}/b^{2} = 1. To obtain the equation of the curve in the form y = f(x) we must “solve” the equation F(x, y) = 0 for y. In Volume I we considered the special problem of finding the inverse of a function y = f(x), that is, the problem of solving the equation F(x, y) = y—f(x) = 0 for the variable x.

## Keywords

Differential Form Tangent Plane Double Point Parametric Representation Differential Calculus
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© Springer-Verlag Berlin Heidelberg 2000