Instructional Video
Sophia Learning

Sophia: Multiply and Substitute Method: Lesson 3

9th - 10th
The method of multiplying a function by a value of one then substituting to find an indeterminate limit is discussed here. This lesson is 3 of 5 in the series titled "Multiply and Substitute Method."
Instructional Video
Sophia Learning

Sophia: Multiply and Substitute Method: Lesson 1

9th - 10th
The method of multiplying a function by a value of one then substituting to find an indeterminate limit is discussed here. This lesson is 1 of 5 in the series titled "Multiply and Substitute Method."
Instructional Video
Sophia Learning

Sophia: Multiplying to Find an Indeterminate Limit: Lesson 2

9th - 10th
This lesson shows how an indeterminate limit may be found by first multiplying the numerator and denominator of the function by a carefully picked factor. It is 2 of 8 in the series titled "Multiplying to Find an Indeterminate Limit."
Instructional Video
Sophia Learning

Sophia: Multiplying to Find an Indeterminate Limit: Lesson 7

9th - 10th
This lesson shows how an indeterminate limit may be found by first multiplying the numerator and denominator of the function by a carefully picked factor. It is 7 of 8 in the series titled "Multiplying to Find an Indeterminate Limit."
Instructional Video
Sophia Learning

Sophia: Multiplying to Find an Indeterminate Limit: Lesson 8

9th - 10th
This lesson shows how an indeterminate limit may be found by first multiplying the numerator and denominator of the function by a carefully picked factor. It is 8 of 8 in the series titled "Multiplying to Find an Indeterminate Limit."
Instructional Video
Sophia Learning

Sophia: Multiplying to Find an Indeterminate Limit: Lesson 1

9th - 10th
This lesson shows how an indeterminate limit may be found by first multiplying the numerator and denominator of the function by a carefully picked factor. It is 1 of 8 in the series titled "Multiplying to Find an Indeterminate Limit."
Instructional Video
Sophia Learning

Sophia: Secant Lines: Lesson 2

9th - 10th
This lesson introduces the concept of secant lines. It is 2 of 5 in the series titled "Secant Lines."
Instructional Video
Sophia Learning

Sophia: Secant Lines: Lesson 1

9th - 10th
This lesson introduces the concept of secant lines. It is 1 of 5 in the series titled "Secant Lines."
Instructional Video
Sophia Learning

Sophia: Second Form of a Derivative: Lesson 2

9th - 10th
This lesson defines the derivative in terms of a limit, as two points on a function get closer together. It is 2 of 4 in the series titled "Second Form of a Derivative."
Instructional Video
Sophia Learning

Sophia: Second Form of a Derivative: Lesson 3

9th - 10th
This lesson defines the derivative in terms of a limit, as two points on a function get closer together. It is 3 of 4 in the series titled "Second Form of a Derivative."
Instructional Video
Sophia Learning

Sophia: Second Form of a Derivative: Lesson 1

9th - 10th
This lesson defines the derivative in terms of a limit, as two points on a function get closer together. It is 1 of 4 in the series titled "Second Form of a Derivative."
Instructional Video
Sophia Learning

Sophia: Trigonometric Limits: Lesson 2

9th - 10th Standards
This lesson explores the possibility of taking the limit of a trigonometric function at a given point. It is 2 of 5 in the series titled "Trigonometric Limits."
Instructional Video
Sophia Learning

Sophia: Trigonometric Limits: Lesson 4

9th - 10th Standards
This lesson explores the possibility of taking the limit of a trigonometric function at a given point. It is 4 of 5 in the series titled "Trigonometric Limits."
Instructional Video
Sophia Learning

Sophia: Trigonometric Limits: Lesson 1

9th - 10th Standards
This lesson explores the possibility of taking the limit of a trigonometric function at a given point. It is 1 of 5 in the series titled "Trigonometric Limits."
Instructional Video
Sophia Learning

Sophia: Undefined and Indeterminate Limit Values: Lesson 2

9th - 10th
The concepts of undefined and indeterminate limits, and their dependence on the values of the numerator and denominator of a rational function are discussed here. This lesson is 2 of 5 in the series titled "Undefined and Indeterminate...
Instructional Video
Sophia Learning

Sophia: Undefined and Indeterminate Limit Values: Lesson 3

9th - 10th
The concepts of undefined and indeterminate limits, and their dependence on the values of the numerator and denominator of a rational function are discussed here. This lesson is 3 of 5 in the series titled "Undefined and Indeterminate...
Instructional Video
Sophia Learning

Sophia: Undefined and Indeterminate Limit Values: Lesson 4

9th - 10th
The concepts of undefined and indeterminate limits, and their dependence on the values of the numerator and denominator of a rational function are discussed here. This lesson is 4 of 5 in the series titled "Undefined and Indeterminate...
Instructional Video
Sophia Learning

Sophia: Undefined and Indeterminate Limit Values: Lesson 5

9th - 10th
The concepts of undefined and indeterminate limits, and their dependence on the values of the numerator and denominator of a rational function are discussed here. This lesson is 5 of 5 in the series titled "Undefined and Indeterminate...
Instructional Video
Sophia Learning

Sophia: Undefined and Indeterminate Limit Values: Lesson 1

9th - 10th
The concepts of undefined and indeterminate limits, and their dependence on the values of the numerator and denominator of a rational function are discussed here. This lesson is 1 of 5 in the series titled "Undefined and Indeterminate...
Instructional Video
Sophia Learning

Sophia: Using a Function to Find a Limit: Lesson 2

9th - 10th
Given a sequence, this lesson demonstrates how to relate it to a function to find the limit. It is 2 of 7 in the series titled "Using a Function to Find a Limit."
Instructional Video
Sophia Learning

Sophia: Using a Function to Find a Limit

9th - 10th
Given a sequence, this lesson demonstrates how to relate it to a function to find the limit.
Instructional Video
Sophia Learning

Sophia: Using a Function to Find a Limit: Lesson 4

9th - 10th
Given a sequence, this lesson demonstrates how to relate it to a function to find the limit. It is 4 of 7 in the series titled "Using a Function to Find a Limit."
Instructional Video
Sophia Learning

Sophia: Using a Function to Find a Limit: Lesson 6

9th - 10th
Given a sequence, this lesson demonstrates how to relate it to a function to find the limit. It is 6 of 7 in the series titled "Using a Function to Find a Limit."
Instructional Video
Sophia Learning

Sophia: Convergence at a Limit

11th - 12th
This lesson explains how the left and right limits for a value of the domain of a function relate to the concept of convergence.