§2.5 - Exercises

by Robert Curtis, Bill Davis, and Lee Wayand.

1. Determine the Formula for the Surface

Given to the right is a MathView interactive which includes a set of level curves in the x-y plane.

The interactive is set up to allow for an animation that lifts the set of level curves up to its parent surface.

Your Task: Discover the algebraic formula for the parent surface. Experiment with your guesses using the

zsurface =
entry line.

Copy and paste your formula into the box below to check your answer.

zsurface =

Help for MathView math entry keystrokes

2. Determine the Formula for the Surface

Given to the right is a MathView interactive which includes a set of level curves in the x-y plane.

The interactive is set up to allow for an animation that lifts the set of level curves up to its parent surface.

Your Task: Discover the algebraic formula for the parent surface. Experiment with your guesses using the

zsurface =
entry line.

Copy and paste your formula into the box below to check your answer.

zsurface =

Help for MathView math entry keystrokes

Road Map
  • VR & 3D Calculus Home Page
    • §2.4 -
    • §2.5 - Level Curves
      • §2.5.1 - A Single Level Curve
      • §2.5.2 - The Set of Level Curves
      • §2.5.3, §2.5.4, §2.5.5, §2.5.6, §2.5.7, §2.5.8, §2.5.9
      • §2.5 Exercises
    • §2.6 -

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Core Development Team
  • Robert R. Curtis
  • Phil R. Smith
  • Christopher A. Barker
  • Diane Welden Housken
  • Tim Lance
  • Bob Stein
  • Donald Hartig
  • Lee Wayand
  • Charlene Beckmann
  • Bill Davis
  • Paul Latiolais
  • Dennis Sentilles
  • Carmen Artino
  • Michael Colvin


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