Ex 5.1, 18 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at March 20, 2018 by Teachoo
Transcript
Ex 5.1, 18 For what value of λ is the function defined by 𝑓 𝑥= λ 𝑥2−2𝑥, 𝑖𝑓 𝑥≤0&4𝑥−1, 𝑖𝑓 𝑥>0 continuous at x = 0? What about continuity at x = 1? We have, 𝑓 𝑥= λ 𝑥2−2𝑥, 𝑖𝑓 𝑥≤0&4𝑥−1, 𝑖𝑓 𝑥>0 (i) At 𝒙=𝟎 f is continuous at 𝑥=0 if L.H.L = R.H.L = 𝑓 0 i.e. if limx→ 0− 𝑓 𝑥 = limx→ 0+ 𝑓 𝑥 = 𝑓 0 Thus, L.H.L ≠ R.H.L ∴ f is not continuous at x = 0. So, for any value of λ∈𝐑 , f is discontinuous at x = 0. (ii) At 𝒙=𝟏 𝑓 𝑥 = 4𝑥+1 f is continuous at 𝑥=1 if limx→1 𝑓 𝑥 = 𝑓 1
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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.