Continuity and Differentiability

IIT-JEE · Class 12 · Mathematics

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What’s covered

  • topics
    • Continuity of a Function
      • continuity
      • discontinuity and its types
      • directional continuity
      • continuity in an interval
      • continuity of functions obtained by algebraic operations
    • Continuity of Specific Functions
      • continuity involving the greatest integer function
      • signum function
      • limit at infinity
      • functions defined differently for rational and irrational values
      • continuity of composite functions
    • Intermediate Value Theorem
      • statement and applications
    • Differentiability
      • definition
      • differentiability and continuity
      • reasons for non-differentiability
      • differentiability in an interval
    • Examining Differentiability
      • differentiability using differentiation and graphs
      • differentiability of functions obtained by algebraic operations
      • continuity of the derivative