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Example 8 - Discuss continuity of f(x) = x3 + x2 - 1 - Examples

Example 8 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Example 8 Discuss the continuity of the function f given by 𝑓 (π‘₯)= π‘₯3 + π‘₯2 βˆ’ 1.Given 𝑓(π‘₯)= π‘₯3 + π‘₯2 βˆ’ 1. To check continuity of 𝑓(π‘₯), We check it’s if it is continuous at any point x = c Let c be any real number f is continuous at π‘₯ =𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) (π‘₯3 + π‘₯2 βˆ’ 1) Putting π‘₯=𝑐 = c3 +𝑐2 βˆ’ 1 𝒇(𝒄) =𝑐3 +𝑐2 βˆ’ 1 Since, L.H.S = R.H.S ∴ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βˆˆπ‘ ∴ f is continuous for every real number.

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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.