Calculus › Section B · Limits › Topic B.1
A preview of calculus: tangent lines and area
How steep is a curve at one exact point? How much area sits under a curved shape? Both questions lie beyond algebra, and both are answered by one new idea: the limit.
In this topic
- Two questions algebra cannot answer
- Average rate of change: the secant line
- The tangent line problem
- Worked example: tangent to y = x² at (2, 4)
- Seeing the limit in a table
- Velocity and other rates of change
- Worked example: a ball thrown upward
- The area problem
- Worked example: estimating an area
- Two problems, one subject
- Common mistakes to avoid
- Key takeaways
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Standards: 1