Solved Problems for Implicit and Parametric Functions

If you wish to simultaneously follow another text on this topic in a separate window, click here for Theory.

• Problem: Express the implicit curve given by (y − 1)² = 4 − ln(x) as a function y = y(x) on some neighborhood of the point (1,−1).

• Problem: Prove that the equation y³ − 3xy = 1 defines a function y = y(x) on some neighborhood of the point (0,1).

• Problem: Identify the shape of the parametric curve
  x = e^t − 1,
  y = e^2t − 2e^t for t real.