Example 20 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at April 13, 2021 by Teachoo
Transcript
Example 20 Show that the function f defined by f (x) = |1โ ๐ฅ + | ๐ฅ ||, where x is any real number is a continuousGiven ๐(๐ฅ) = |(1โ๐ฅ+|๐ฅ|)| Let ๐(๐) = 1โ๐ฅ+|๐ฅ| & ๐(๐) = |๐ฅ| Then , ๐๐๐(๐) = โ(๐(๐ฅ)) = โ(1โ๐ฅ+|๐ฅ|) = |(1โ๐ฅ+|๐ฅ|)| = ๐(๐) We know that, Modulus function is continuous โด ๐(๐) = |๐ฅ| is continuous Also, ๐(๐) = (๐โ๐)+|๐| Since (1โ๐ฅ) is a polynomial & every polynomial function is continuous โด (๐โ๐) is continuous Also, |๐| is also continuous Since Sum of two continuous function is also continuous Thus, ๐(๐ฅ) = 1โ๐ฅ+|๐ฅ| is continuous . Hence, ๐(๐ฅ) & โ(๐ฅ) are both continuous . We know that If two function of ๐(๐ฅ) & โ(๐ฅ) both continuous, then their composition ๐๐๐(๐) is also continuous Hence, ๐(๐) is continuous .
Examples
Example 1
Example 2
Example 3
Example 4 Important
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15 Important
Example 16
Example 17 Important
Example 18
Example 19
Example 20 Important You are here
Example 21
Example 22
Example 23 Important
Example 24
Example 25
Example 26 Important
Example 27
Example 28
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
Example 35
Example 36 Important
Example 37 Important
Example 38
Example 39 Important
Example 40
Example 41 Important
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)
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.