Ex 12.1, 18 - Chapter 12 Class 11 Limits and Derivatives

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Ex 12.1, 18 Evaluate the Given limit: lim﷮x→0﷯ ax+x cos﷮x﷯﷮b sin﷮x﷯﷯ lim﷮x→0﷯ ax + x cos﷮x﷯﷮b sin﷮x﷯﷯ = lim﷮x→0﷯ x (a + cos﷮x)﷯﷮b sin﷮x﷯﷯ = lim﷮x→0﷯ (a + cos﷮x) ﷯﷮𝑏﷯ × 𝑥﷮ sin﷮𝑥﷯﷯﷯ = lim﷮x→0﷯ (a + cos﷮x) ﷯﷮𝑏﷯÷ sin﷮𝑥﷯﷮𝑥﷯﷯ = lim﷮x→0﷯ (a + cos﷮x) ﷯﷮𝑏﷯﷯ ÷ lim﷮x→0﷯ sin﷮𝑥﷯﷮𝑥﷯﷯ = lim﷮x→0﷯ a + cos﷮x ﷯﷮𝑏﷯﷯ ÷ 1 = lim﷮x→0﷯ a + cos﷮x ﷯﷮𝑏﷯ = lim﷮x→0﷯ a + cos﷮x ﷯﷮𝑏﷯ Putting x = 0 = 𝑎 + cos﷮0﷯﷮𝑏﷯ = 𝒂 + 𝟏﷮𝒃﷯

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