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Example 9 - Discuss continuity of f(x) = 1/x - Chapter 5

Example 9 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Example 9 - Chapter 5 Class 12 Continuity and Differentiability - Part 3


Transcript

Example 9 Discuss the continuity of the function f defined by 𝑓 (π‘₯) = 1/π‘₯ , π‘₯ β‰  0. Given 𝑓 (π‘₯) = 1/π‘₯ At 𝒙 = 𝟎 𝑓 (0) = 1/0 = ∞ Hence, 𝑓(π‘₯) is not defined at 𝒙=𝟎 By definition, 𝑓 (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‘₯ =𝑐 if , (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (Except 0) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) 1/π‘₯ Putting π‘₯ =𝑐 = 1/𝑐 𝒇(𝒄) =1/𝑐 " " Thus, we can write that f is continuous for all 𝒙 βˆˆπ‘βˆ’{𝟎} Thus, we can write that f is continuous for all 𝒙 βˆˆπ‘βˆ’{𝟎}

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.