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Ex 5.1 ,4 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Checking continuity at any point
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
Transcript
Ex 5.1, 4 Prove that the function f (x) = π₯^π is continuous at x = n, where n is a positive integer.π(π₯) is continuous at x = n if limβ¬(xβπ) π(π₯)= π(π) Since, L.H.S = R.H.S β΄ Function is continuous at x = n (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(xβπ) π₯^π Putting π₯=π = π^π π(π) = π^π β΄ Thus limβ¬(xβπ) f(x) = f(n) Hence, f(x) = xn is continuous at x = n
