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Calculus

Limits

Learn to read what a function is heading toward, even when direct substitution fails.

Goal:

Understand limits

3Lessons
6Micro-lessons
BeginnerDifficulty
Lesson 1

The Idea of Approaching

See what “getting close” means for inputs and outputs.

Start2 Micro-lessons

Micro lesson 1
Close, Not Equal
Micro lesson 2
Plug In When It’s Smooth
Lesson 2

One-Sided Thinking

Handle approach from the left and from the right.

Start2 Micro-lessons

Micro lesson 1
Left Side Approach
Micro lesson 2
When Both Sides Agree
Lesson 3

Reading Behavior

Use graphs and real situations to judge limits.

Start2 Micro-lessons

Micro lesson 1
Holes and Jumps
Micro lesson 2
Tolerance: How Close Is Close?