Ex 13.1, 15 - Evalaute: lim x->pi  sin (pi -x)/pi (pi-x) - Limits - Of Trignometric functions

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  1. Chapter 13 Class 11 Limits and Derivatives
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Ex13.1, 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﷯

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