Instructional Video
Sophia Learning

Sophia: Convergence at a Limit: Lesson 2

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. It is 2 of 5 in the series titled "Convergence at a Limit." [3:27]
Instructional Video
Sophia Learning

Sophia: Convergence at a Limit: Lesson 3

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. It is 3 of 5 in the series titled "Convergence at a Limit." [1:56]
Instructional Video
Sophia Learning

Sophia: Finding an Indeterminate Limit With a T Chart: Lesson 4

9th - 10th
This lesson shows how an indeterminate limit may be found for an element of the domain of a function by constructing a T chart. It is 4 of 7 in the series titled "Finding an Indeterminate Limit with a T Chart."
Instructional Video
Sophia Learning

Sophia: Finding a Vertical Tangent: Lesson 3

9th - 10th
This lesson shows how to recognize when a tangent line is vertical by determining if the slope is undefined. It is 3 of 7 in the series titled "Finding a Vertical Tangent."
Instructional Video
Sophia Learning

Sophia: Multiply and Substitute Method: Lesson 4

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 4 of 5 in the series titled "Multiply and Substitute Method."
Instructional Video
Sophia Learning

Sophia: Limits of Convergent Series

9th - 10th
This lesson teaches students to find the limits of sequences that converge.
Instructional Video
Khan Academy

Khan Academy: Vi Hart: Rhapsody on the Proof of Pi = 4

9th - 10th
Video explores properties of circles and what is wrong with the proof that pi is equal to four. [5:55]