Ex 13.1, 14 - Evaluate: lim x->0 sin ax/sin bx - Class 11 CBSE - Limits - Of Trignometric functions

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  1. Chapter 13 Class 11 Limits and Derivatives
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Ex13.1, 14 Evaluate the Given limit: lim﷮x→0﷯ sin﷮ax ﷯﷮sin bx﷯, a, b ≠ 0 lim﷮x→0﷯ sin﷮ax ﷯﷮sin bx﷯ = lim﷮x→0﷯ sin ax × lim﷮x→0﷯ 1﷮ sin﷮𝑏𝑥﷯﷯ Multiplying & dividing by ax = 𝐥𝐢𝐦﷮𝐱→𝟎﷯ 𝐬𝐢𝐧﷮𝒂𝒙﷯﷮𝒂𝒙﷯ × lim﷮x→0﷯ 𝑎𝑥﷮ sin﷮𝑏𝑥﷯﷯ = 1 × lim﷮x→0﷯ 𝑎𝑥﷮ sin﷮𝑏𝑥﷯﷯ = lim﷮x→0﷯ 𝑎𝑥﷮ sin﷮𝑏𝑥﷯﷯ Multiplying & dividing by bx = lim﷮x→0﷯ 𝑎𝑥﷮ sin﷮𝑏𝑥﷯﷯ × 𝑏𝑥﷮𝑏𝑥﷯ = lim﷮x→0﷯ 𝑏𝑥﷮ sin﷮𝑏𝑥﷯﷯ × 𝑎𝑥﷮𝑏𝑥﷯ = lim﷮x→0﷯ 𝑏𝑥﷮ sin﷮𝑏𝑥﷯﷯ × 𝑎﷮𝑏﷯ = 𝑎﷮𝑏﷯ lim﷮x→0﷯ 𝑏𝑥﷮ sin﷮𝑏𝑥﷯﷯ = 𝑎﷮𝑏﷯ ÷ 𝐥𝐢𝐦﷮𝐱→𝟎﷯ 𝐬𝐢𝐧﷮𝒃𝒙﷯﷮𝒃𝒙﷯ = 𝑎﷮𝑏﷯ ÷ 1 = 𝒂﷮𝒃﷯

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