JEE Advanced Math — Limits, Continuity and Differentiability
Limits, continuity, and differentiability for JEE Advanced aspirants.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Evaluate indeterminate-form limits using Taylor and Maclaurin expansions to required precision [Evaluate]
- Apply the Intermediate Value Theorem to argue about existence of roots in given intervals [Apply]
- Analyze differentiability of piecewise functions and functions defined via functional equations [Analyze]
- Apply Leibniz's rule for higher-order derivatives of products [Apply]
- Investigate functions that are continuous but not differentiable and identify counterexamples [Analyze]
- Solve JEE Advanced multi-step and paragraph problems on limits and differentiability [Evaluate]
📚 Chapters
- Limits — Standard Forms and Indeterminate Forms
- L'Hopital's Rule and Series Expansions
- Limits via Squeeze Theorem
- Continuity — Definitions and Theorems
- Discontinuities and Removability
- Intermediate Value Theorem
- Differentiability and Its Subtleties
- Differentiation of Standard and Implicit Functions
- Higher Order Derivatives and Leibniz Rule
- Functional Equations and Differentiability
- Mixed Advanced Problems
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