Ex 12.1, 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.