Introducing your new favourite teacher - Teachoo Black, at only βΉ83 per month
Example 12 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 12, 2021 by Teachoo
Checking continuity using LHL and RHL
Example 12
You are here
Example 10
Example 13 Important
Ex 5.1, 10
Ex 5.1, 11
Ex 5.1 ,6
Ex 5.1, 13
Ex 5.1, 12 Important
Example 11 Important
Example 7
Ex 5.1, 3 (a)
Ex 5.1, 14
Ex 5.1, 16
Ex 5.1, 15 Important
Ex 5.1 ,7 Important
Ex 5.1, 25
Ex 5.1, 23
Ex 5.1, 24 Important
Ex 5.1 ,8
Ex 5.1, 9 Important
Ex 5.1, 29
Ex 5.1, 27
Ex 5.1, 28 Important
Ex 5.1, 17 Important
Ex 5.1, 18 Important
Ex 5.1, 26 Important
Ex 5.1, 30 Important
Example 15 Important
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
Example 12 Discuss the continuity of the function defined by π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€ π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€ 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 > 0 Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous β΄ f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = βx + 2 Since this a polynomial It is continuous β΄ f(x) is continuous for x > 0 Hence, π is continuous for all Real points except 0. Thus, π is continuous for π βπβ{π}
