IB Math AI 5.1 - Limits Notes

This IB Maths AI SL 5.1 – Limits, Rate of Change & Derivatives resource introduces the core ideas of calculus through clear, intuitive development. Students first explore limits as the value a function approaches near a point, even when the function may be undefined, building understanding of function behaviour at “problem points” .

The lesson then links gradients of lines to average rate of change on curves using secant lines, before introducing instantaneous rate of change and the derivative through the difference quotient and limit notation. Students learn to interpret the derivative as the gradient at a single point and become familiar with standard derivative notation .

Structured notes, guided examples, and an optional extension on the formal definition of limits support both core SL understanding and deeper conceptual insight, preparing students for further calculus applications in IB Mathematics AI SL.

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