Limits
Understand the limits of sequences and functions, and build the foundation for calculus.
Sequences
The Index
Recursive Sequences
Increasing or Decreasing
Bounded
Decimal Expansions
Approximating a Number
Level Check
Sequences as Functions
Properties on a Graph
Starting Index
Arithmetic Sequences
Geometric Sequences
Geometric Behavior
Level Check
Hitting the Target
The Limit
Any Target Size
Looping Toward the Target
Comparing Powers
Comparing Coefficients
Limits on a Graph
Finitely Many Exceptions
Leaving the Target
The Limit Does Not Exist
Goes To Infinity
Goes To Negative Infinity
Infinity on a Graph
Comparing Geometric Sequences
Vertical Asymptotes
(Coming soon)
The Floor Function
(Coming soon)
Approaching a Point
(Coming soon)
One-Sided Limits
(Coming soon)
Limit Versus Value
(Coming soon)
Building Functions
(Coming soon)
Mismatched Sides
(Coming soon)
Unbounded
(Coming soon)
Oscillations
(Coming soon)
Limits from Graphs
(Coming soon)
Sum of Limits
(Coming soon)
Dangerous Sums
(Coming soon)
Products of Limits
(Coming soon)
Dangerous Products
(Coming soon)
Powers of Limits
(Coming soon)
Dangerous Powers
(Coming soon)
Converging at Infinity
(Coming soon)
Infinity at Infinity
(Coming soon)
Oscilating at Infinity
(Coming soon)
Continuity at a Point
(Coming soon)
Removable Discontinuities
(Coming soon)
Jump Discontinuities
(Coming soon)
Discontinuities at Asymptotes
(Coming soon)
Eliminating Discontinuities
(Coming soon)
Open and Closed Intervals
(Coming soon)
Continuous on an Interval
(Coming soon)
Continuous Everywhere
(Coming soon)
Algebra of Continuity
(Coming soon)
Composition of Functions
(Coming soon)
Trigonometric Functions
(Coming soon)
Polynomial Functions
(Coming soon)
Rational Functions
(Coming soon)
Exponential and Logarithmic Functions
(Coming soon)
Flipping Sign
(Coming soon)
Finding the Crossing
(Coming soon)
The Intermediate Value Theorem
(Coming soon)
Iterating the IVT
(Coming soon)
Course description
In this course, you'll build an understanding of limits — a foundational idea in calculus. Starting with sequences on number lines and graphs, you'll develop intuition for convergence before formalizing what it means for a limit to exist. You'll then extend these ideas to functions, explore continuity, and apply the Intermediate Value Theorem.
Topics covered
- Sequences
- Limits of Sequences
- Limits of Functions
- Convergence
- Divergence
- Continuity of Functions
- Intermediate Value Theorem
- Euler's Number
Prerequisites and next steps
You should start the course with a foundation in algebra and the basics of functions, including graphing equations. When you finish, you'll be well-prepared to learn about derivatives and integrals.