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Last updated at Aug. 19, 2021 by

Β

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Ex 5.1, 3 Examine the following functions for continuity. (b) f (x) = 1/(π₯ β 5) , x β 5 f (x) = 1/(π₯ β 5) At x = 5 f (x) = 1/(5 β 5) = 1/0 = β Hence, f(x) is not defined at x = 5 So, we check for continuity at all points except 5 Let c be any real number except 5. f is continuous at π₯ = π if (π₯π’π¦)β¬(π±βπ) π(π) = π(π) LHS (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(π₯βΆπ)β‘γ1/(π₯ β 5)γ = 1/(π β 5) RHS π(π) = 1/(π β 5) Since, L.H.S = R.H.S β΄ Function is continuous at x = c (except 5) Thus, we can write that f is continuous for all real numbers except 5 β΄ f is continuous at each π± β R β {π}

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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.