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Last updated at April 16, 2024 by Teachoo

Example 9 Discuss the continuity of the function f defined by π (π₯) = 1/π₯ , π₯ β 0. Given π (π₯) = 1/π₯ At π = π π (0) = 1/0 = β Hence, π(π₯) is not defined at π=π By definition, π (π₯) = 1/π₯ , π₯ β 0. So, we check for continuity at all points except 0. Let c be any real number except 0. f is continuous at π₯ =π if , (π₯π’π¦)β¬(π±βπ) π(π)=π(π) L.H.S L.H.S (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(xβπ) 1/π₯ Putting π₯ =π = 1/π R.H.S π(π) =1/π " " Since, L.H.S = R.H.S β΄ Function is continuous at x = c (Except 0) Since, L.H.S = R.H.S β΄ Function is continuous at x = c (Except 0) Thus, we can write that f is continuous for all π βπβ{π}