1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise

Transcript

Example 12 Discuss the continuity of the function defined by ๐๏ท๐ฅ๏ทฏ=๏ท๏ท& ๐ฅ+2, ๐๐ ๐ฅ<0๏ทฎ&โ๐ฅ+2, ๐๐ ๐ฅ>0๏ทฏ๏ทฏ We have, ๐๏ท๐ฅ๏ทฏ=๏ท๏ท& ๐ฅ+2, ๐๐ ๐ฅ<0๏ทฎ&โ๐ฅ+2, ๐๐ ๐ฅ>0๏ทฏ๏ทฏ Here, the given function is not defined at ๐ฅ=0. So, we check continuity for all real numbers except 0. Case 1 Let ๐ฅ=๐ where ๐<0. ๐๏ท๐ฅ๏ทฏ=๐ฅ+2 ๐ is continuous at ๐ฅ=๐ if ๏ทlim๏ทฎxโ๐๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท๐๏ทฏ Hence ๏ทlim๏ทฎxโ๐๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท๐๏ทฏ โ ๐ is continuous at ๐ฅ=๐ where ๐<0. โ ๐ is continuous at all Real points less than 0. Case 2 Let ๐ฅ=๐ where ๐<0. ๐๏ท๐ฅ๏ทฏ=โ๐ฅ+2 ๐ is continuous at ๐ฅ=๐ if ๏ทlim๏ทฎxโ๐๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท๐๏ทฏ Hence ๏ทlim๏ทฎxโ๐๏ทฏ ๐๏ท๐ฅ๏ทฏ= ๐๏ท๐๏ทฏ โ ๐ is continuous at ๐ฅ=๐ where ๐>0. โ ๐ is continuous for all Real points greater than 0. Hence, ๐ is continuous for all Real points except 0. โ ๐ is continuous for ๐ โ๐โ๏ท๐๏ทฏ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.