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Continuity And Differentiability — Revision Notes

Tripura JEE · Mathematics

Free Continuity And Differentiability revision notes for Tripura JEE Mathematics 2026 — key concepts, formulas, and definitions for quick revision.

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A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
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Revision Notes — Continuity And Differentiability

Key concepts, formulas, and definitions from Continuity And Differentiability for Tripura JEE Mathematics preparation.

Key Topics to Revise

1

Continuity of Functions

  • A function f(x) is continuous at x = a if lim(x→a) f(x) = f(a)
  • For continuity, three conditions must be satisfied: function must be defined at the point, limit must exist, and limit must equal function value
  • Continuity can be checked using left-hand limit (LHL) and right-hand limit (RHL)
2

Differentiability of Functions

  • A function is differentiable at x = a if both left-hand derivative (LHD) and right-hand derivative (RHD) exist and are equal
  • Differentiability implies continuity, but continuity does not imply differentiability
  • Common non-differentiable points: sharp corners, vertical tangents, and discontinuities
3

Derivatives of Inverse Trigonometric Functions

  • Inverse trigonometric functions have specific derivative formulas that must be memorized
  • Domain restrictions are crucial when working with inverse trigonometric functions
  • Chain rule applications are common with inverse trigonometric functions
4

Exponential and Logarithmic Functions

  • Exponential function eˣ is its own derivative: d/dx(eˣ) = eˣ
  • Natural logarithm derivative: d/dx(ln x) = 1/x for x > 0
  • Chain rule is frequently needed with exponential and logarithmic functions

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Key Concepts

A function f(x) is continuous atThree main types existA function is differentiable at xIf y = f(g(x))Key derivatives

Frequently Asked Questions

What topics are covered in Continuity And Differentiability for Tripura JEE?
Continuity And Differentiability is an important chapter in Tripura JEE Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Continuity of Functions, Differentiability of Functions, Derivatives of Inverse Trigonometric Functions, Exponential and Logarithmic Functions.
How important is Continuity And Differentiability for Tripura JEE?
Continuity And Differentiability is a frequently tested chapter in Tripura JEE Mathematics. Questions from this chapter appear regularly in previous year papers. There are 455 practice questions available for this chapter.
How to prepare Continuity And Differentiability for Tripura JEE?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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