TANGENT PLANES TO SURFACES

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Introduction

In earlier calculus classes, we learned that a tangent line (at point x) could be found by differentiating a function with respect to x (i.e. f(x)=3x^2, f'(x)=6x). In calculus III, tangent surfaces (points, lines, planes, surfaces) become a more vital part of the mathematics covered during the year. This lab has been written to help accelerate and deepen the understanding of tangents. In this lab we will examine the three main types of functions and their tangents: explicit, parametric, and implicit. To help ease your way, we have written three Maple programs: GraphTan, ParamTan, and ImplicitTan.

Tangent Planes to a Graph
Tangent Planes to a Parametric Surface
Tangent Planes to an Implicitly Defined Surface
When Problems Arise
An Application of the Tangent Plane

Next: Tangent Planes to a Graph

TANGENT PLANES TO SURFACES

Introduction

Contents