You are here
Ex 5.1, 32 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 11, 2026 by Teachoo
Continuity of composite functions
Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
-
Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem
Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Transcript
Ex 5.1, 32 Show that the function defined by ๐ (๐ฅ)= |cosโก๐ฅ | is a continuous function.๐(๐ฅ) = |cosโก๐ฅ | Let ๐(๐) = |๐ฅ| & ๐(๐) = cosโก๐ฅ Now, ๐๐๐(๐) = g(โ(๐ฅ)) = ๐(cosโก๐ฅ ) = |cosโก๐ฅ | = ๐(๐) Hence, ๐(๐ฅ) = ๐๐โ(๐ฅ) We know that, ๐(๐) = cosโก๐ฅ is continuous as cos is continuous & ๐(๐) = |๐ฅ| is continuous as it is a modulus function Hence, ๐(๐ฅ) & โ(๐ฅ) are both continuous . We know that If two function of ๐(๐ฅ) & โ(๐ฅ) both continuous, then their composition ๐๐๐(๐) is also continuous Hence, ๐(๐) is continuous . .
