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Ex 5.1, 31 - 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
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Transcript
Ex 5.1, 31 Show that the function defined by ๐(๐ฅ)=cosโก(๐ฅ^2 ) is a continuous function.๐(๐ฅ) = cosโก(๐ฅ^2 ) Let ๐(๐) = cosโก๐ฅ & ๐(๐) = ๐ฅ^2 Now, ๐๐๐(๐) = g(โ(๐ฅ)) = ๐(๐ฅ^2 ) = cosโก(๐ฅ^2 ) = ๐(๐) Hence, ๐(๐ฅ) = ๐๐โ(๐ฅ) We know that ๐(๐) = cosโก๐ฅ is continuous as cos x is always continuous & ๐(๐) = ๐ฅ^2 is continuous as it is a polynomial 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 .
