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Example 9 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at December 16, 2024 by Teachoo
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Chapter 5 Class 12 Continuity and Differentiability
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Example 9 Discuss the continuity of the function f defined by š (š„) = 1/š„ , š„ ā 0. Given š (š„) = 1/š„ At š = š š (0) = 1/0 = ā Hence, š(š„) is not defined at š=š By definition, š (š„) = 1/š„ , š„ ā 0. So, we check for continuity at all points except 0. Let c be any real number except 0. f is continuous at š„ =š if , (š„š¢š¦)ā¬(š±āš) š(š)=š(š) L.H.S L.H.S (š„š¢š¦)ā¬(š±āš) š(š) = limā¬(xāš) 1/š„ Putting š„ =š = 1/š R.H.S š(š) =1/š " " Since, L.H.S = R.H.S ā“ Function is continuous at x = c (Except 0) Since, L.H.S = R.H.S ā“ Function is continuous at x = c (Except 0) Thus, we can write that f is continuous for all š āšā{š}
