Example 12 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Checking continuity using LHL and RHL
Example 12
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Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
- Checking continuity at any point
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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
Example 12 Discuss the continuity of the function defined by 𝑓(𝑥)={█(& 𝑥+2, 𝑖𝑓 𝑥<0@&−𝑥+2, 𝑖𝑓 𝑥>0)┤ 𝑓(𝑥)={█(& 𝑥+2, 𝑖𝑓 𝑥<0@&−𝑥+2, 𝑖𝑓 𝑥>0)┤ Here, function is not defined for x = 0 So, we do not check continuity there We check continuity for different values of x When x < 0 When x > 0Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = −x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x > 0 Hence, 𝑓 is continuous for all Real points except 0. Thus, 𝒇 is continuous for 𝒙 ∈𝐑−{𝟎}
