Ex 5.1, 26 - Find values of k so that f(x) = k cos x / pi - 2x - Checking continuity using LHL and RHL

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.1, 26 Find the values of k so that the function f is continuous at the indicated point 𝑓 𝑥﷯= 𝑘 cos﷮𝑥﷯﷮𝜋 − 2𝑥 ﷯ , 𝑖𝑓 𝑥≠ 𝜋﷮2﷯﷮& 3, 𝑖𝑓 𝑥= 𝜋﷮2﷯﷯﷯ at 𝑥 = 𝜋﷮2﷯ Given that function is continuous at 𝑥 = 𝜋﷮2﷯ 𝑓 is continuous at 𝑥 = 𝜋﷮2﷯ if L.H.L = R.H.L = 𝑓 𝜋﷮2﷯﷯ i.e. lim﷮x→ 𝜋﷮2﷯﷮−﷯﷯ 𝑓 𝑥﷯= lim﷮x→ 𝜋﷮2﷯﷮+﷯﷯ 𝑓(𝑥)= 𝑓 𝜋﷮2﷯﷯ i.e. lim﷮x→ 𝜋﷮2﷯﷮−﷯﷯ 𝑓 𝑥﷯= lim﷮x→ 𝜋﷮2﷯﷮+﷯﷯ 𝑓(𝑥)=3 Let y = 𝜋﷮2﷯ −𝑥 as x→ 𝜋﷮2﷯ y→ 𝜋﷮2﷯ − 𝜋﷮2﷯ y→ 0 So, our equation becomes = 𝑘﷮2﷯ lim﷮y→0﷯ sin﷮𝑦﷯﷮𝑦﷯ = 𝑘﷮2﷯ (1) = 𝑘﷮2﷯ Hence, L.H.L = 𝑘﷮2﷯ & R.H.L = 𝑘﷮2﷯ Now, L.H.L = R.H.L = 3 ∴ L.H.L = 3 Putting values 𝑘﷮2﷯ = 3 k = 3 × 2 k = 6 Hence k = 6

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.