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Example 7 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 12, 2021 by Teachoo
Transcript
Example 7 Is the function defined by f (x) = |x|, a continuous function? f(x) = |π₯| = {β(βπ₯, π₯<0@π₯, π₯β₯0)β€ Since we need to find continuity at of the function We check continuity for different values of x When x = 0 When x < 0 When x > 0 Case 1 : When x = 0 f(x) is continuous at π₯ =0 if L.H.L = R.H.L = π(0) if limβ¬(xβ0^β ) π(π₯)=limβ¬(xβ0^+ ) " " π(π₯)= π(0) Since there are two different functions on the left & right of 5, we take LHL & RHL . LHL at x β 0 limβ¬(xβ0^β ) f(x) = limβ¬(hβ0) f(0 β h) = limβ¬(hβ0) f(βh) = limβ¬(hβ0) |ββ| = limβ¬(hβ0) β = 0 RHL at x β 0 limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h) = limβ¬(hβ0) f(h) = limβ¬(hβ0) |β| = limβ¬(hβ0) β = 0 & π(0) = 0 Hence, L.H.L = R.H.L = π(0) β΄ f is continuous at x=0 Case 2 : When x < 0 For x < 0, f(x) = βx Since this a polynomial It is continuous β΄ f(x) is continuous for x < 0 Case 3 : When x > 0 For x > 0, f(x) = x Since this a polynomial It is continuous β΄ f(x) is continuous for x > 0 Hence, π(π₯)= |π₯| is continuous at all points. i.e. f is continuous at π β R.
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Example 7 You are here
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Example 27
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Example 29 (i)
Example 29 (ii) Important
Example 29 (iii) Important
Example 29 (iv)
Example 30 Important
Example 31
Example 32 Important
Example 33 Important
Example 34
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Example 37 Important
Example 38
Example 39 Important
Example 40
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Example 42 Important Deleted for CBSE Board 2022 Exams
Example 43 Deleted for CBSE Board 2022 Exams
Example 44 (i)
Example 44 (ii) Important
Example 44 (iii) Important
Example 45 (i)
Example 45 (ii) Important
Example 45 (iii) Important
Example 46
Example 47 Important
Example 48
Chapter 5 Class 12 Continuity and Differentiability (Term 1)
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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.