Class 12 Mathematics Chapter 5 Continuity and Differentiability – Revision Notes

Quick revision notes for Class 12 Maths Chapter 5 (Continuity and Differentiability). These Class 12 Mathematics Chapter 5 notes are ideal for quick revision just before exams.

Continuity

• f continuous at a: LHL=RHL=f(a).
• Differentiability ⇒ continuity (not vice versa).

Differentiation Rules

• Chain rule: [f(g(x))]’=f'(g(x))g'(x).
• Implicit differentiation: differentiate both sides w.r.t. x, solve for dy/dx.
• d/dx(e^x)=e^x; d/dx(log x)=1/x.
• Logarithmic differentiation for [f(x)]^g(x).

Theorems

• Rolle’s Theorem: f(a)=f(b) ⇒ ∃c with f'(c)=0.
• Mean Value Theorem: f'(c)=[f(b)−f(a)]/(b−a).

One-Line Summary

Continuity requires matching limits and function value; differentiability is a stronger condition implying continuity, governed by chain/implicit/logarithmic differentiation rules and mean value theorems.

Written by Satish

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