Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12



  1. Chapter 5 Class 12 Continuity and Differentiability
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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. Since x – 5 is a polynomial. ∴ f(x) is defined for every real number c. Let us check continuity at x = c f(x) is is continuous at x = c if lim┬(x→𝑐) 𝑓(π‘₯) = 𝑓(𝑐) lim┬(x→𝑐) 𝑓(π‘₯) = lim┬(x→𝑐) (π‘₯3 + π‘₯2 βˆ’ 1) Putting π‘₯=𝑐 = c3 +𝑐2 βˆ’ 1 𝑓(π‘₯)= π‘₯3 + π‘₯2 βˆ’ 1 𝑓(𝑐)=𝑐3 +𝑐2 βˆ’ 1 Since lim┬(x→𝑐) 𝑓(π‘₯) = 𝑓(𝑐) So, f is continuous for x = c, where c is a real number ∴ f is continuous for all real numbers Hence, f is continuous for each x ∈ R

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.