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Continuity And Differentiability — Revision Notes

J&K CET · Mathematics

Free Continuity And Differentiability revision notes for J&K CET 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 J&K CET 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 J&K CET?
Continuity And Differentiability is an important chapter in J&K CET 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 J&K CET?
Continuity And Differentiability is a frequently tested chapter in J&K CET 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 J&K CET?
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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