Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Linear Approximation
Language:
English
Media Formats:
eBook, Interactive

# 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.