Last updated at March 12, 2021 by Teachoo

Transcript

Example 10 Discuss the continuity of the function f defined by π(π₯)={β(&π₯+2, ππ π₯β€1@&π₯β2, ππ π₯>1)β€ π(π₯)={β(&π₯+2, ππ π₯β€1@&π₯β2, ππ π₯>1)β€ Since we need to find continuity at of the function We check continuity for different values of x When x = 1 When x < 1 When x > 1 Case 1 : When x = 1 f(x) is continuous at π₯ =1 if L.H.L = R.H.L = π(1) if limβ¬(xβ1^β ) π(π₯)=limβ¬(xβ1^+ ) " " π(π₯)= π(1) Since there are two different functions on the left & right of 1, we take LHL & RHL . LHL at x β 1 limβ¬(xβ1^β ) f(x) = limβ¬(hβ0) f(1 β h) = limβ¬(hβ0) (1ββ)+2 = limβ¬(hβ0) (3ββ) = 3 β 0 = 3 RHL at x β 1 limβ¬(xβ1^+ ) f(x) = limβ¬(hβ0) f(1 + h) = limβ¬(hβ0) (1+β)β2 = limβ¬(hβ0) (β1+β) = β1 + 0 = β1 Since L.H.L β R.H.L f(x) is not continuous at x = 1 Case 2 : When x < 1 For x < 1, f(x) = x + 2 Since this a polynomial It is continuous β΄ f(x) is continuous for x < 1 Case 3 : When x > 1 For x > 1, f(x) = x β 2 Since this a polynomial It is continuous β΄ f(x) is continuous for x > 1 Hence, only π₯=1 is point of discontinuity. β΄ f is continuous at all real numbers except 1 Thus, f is continuous for πβ R β {1}

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10 You are here

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17 Important

Example 18

Example 19

Example 20 Important

Example 21

Example 22

Example 23

Example 24

Example 25

Example 26 Important

Example 27

Example 28

Example 29 Important

Example 30 Important

Example 31

Example 32 Important

Example 33 Important

Example 34

Example 35

Example 36 Important

Example 37 Important

Example 38

Example 39

Example 40

Example 41

Example 42 Important Deleted for CBSE Board 2021 Exams only

Example 43 Deleted for CBSE Board 2021 Exams only

Example 44 Important

Example 45 Important

Example 46

Example 47 Important

Example 48

Chapter 5 Class 12 Continuity and Differentiability

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.