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Ex 13.1, 15 - Evalaute: lim x->pi  sin (pi -x)/pi (pi-x)

Ex 13.1, 15 - Chapter 13 Class 11 Limits and Derivatives - Part 2


Transcript

Ex 13.1, 15 Evaluate the Given limit: lim┬(x→π) (sin (π − x))/(π(π − x)) lim┬(x→π) (sin (π − x))/(π(π − x)) Let y = π – x So, when x → π y → π – π y → 0 So, our equation becomes (𝒍𝒊𝒎)┬(𝒙→𝝅) (𝒔𝒊𝒏 (𝝅 − 𝒙))/(𝝅(𝝅 − 𝒙)) = (𝒍𝒊𝒎)┬(𝒚→𝟎) (𝒔𝒊𝒏 𝒚)/(𝝅 𝒚) = 1/𝜋 lim┬(y→0) (sin 𝑦)/y = 1/𝜋 × 1 = 𝟏/𝝅 Using lim┬(x→0) sin⁡𝑥/𝑥 = 1 Replace x with y

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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.