Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Linear Approximation
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
eBook, Interactive

Education Standards (1)

Linear approximation module

Overview

After completing this section, students should be able to do the following.

  • Define linear approximation as an application of the tangent to a curve.
  • Find the linear approximation to a function at a point and use it to approximate the function value.
  • Identify when a linear approximation can be used.
  • Label a graph with the appropriate quantities used in linear approximation.
  • Find the error of a linear approximation.
  • Compute differentials.
  • Use the second derivative to discuss whether the linear approximation over or underestimates the actual function value.
  • Contrast the notation and meaning of dydy versus ΔyΔy.
  • Understand that the error shrinks faster than the displacement in the input.
  • Justify the chain rule via the composition of linear approximations.

Replacing curves with lines

Ximera Module

Two young mathematicians discuss linear approximation.

Linear approximation

Ximera Module

We use a method called ``linear approximation'' to estimate the value of a (complicated) function at a given point.

Explanation of the product and chain rules

Ximera Module

We give explanation for the product rule and chain rule.