Example 4 - Evaluate (i) lim x->0 sin 4x/sin 2x - Chapter 13 CBSE - Examples

Example 4 - Chapter 13 Class 11 Limits and Derivatives - Part 2

 

 

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Example, 4 Evaluate: (i) lim﷮x→0﷯ sin﷮4x﷯﷮sin 2x﷯ lim﷮x→0﷯ sin﷮4x﷯﷮sin 2x﷯ = lim﷮x→0﷯ sin 4x × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ Multiplying & dividing by 4x = lim﷮x→0﷯ sin 4x . 4𝑥﷮4𝑥﷯ × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ = lim﷮x→0﷯ sin﷮4𝑥﷯﷮4𝑥﷯ . 4x × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ = 𝐥𝐢𝐦﷮𝐱→𝟎﷯ 𝒔𝒊𝒏﷮𝟒𝒙﷯﷮𝟒𝒙﷯ × lim﷮x→0﷯ 4x × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ = 1 × lim﷮x→0﷯ 4x × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ = 1 × lim﷮x→0﷯ 4x × lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ = lim﷮x→0﷯ 1﷮ sin﷮2𝑥﷯﷯ . 4x Multiplying & dividing by 2x = lim﷮x→0﷯ 1﷮sin 2x﷯ × 4x × 2𝑥﷮2𝑥﷯ = lim﷮x→0﷯ 2𝑥﷮sin 2x﷯ × 4𝑥﷮2𝑥﷯ = lim﷮x→0﷯ 2𝑥﷮ sin﷮2𝑥﷯﷯ × 2 = 2 lim﷮x→0﷯ 2𝑥﷮ sin﷮2𝑥﷯﷯ = 2 ÷ 𝐥𝐢𝐦﷮𝐱→𝟎﷯ 𝐬𝐢𝐧﷮𝟐𝒙﷯﷮𝟐𝒙﷯ = 2 ÷ 1 = 2﷮1﷯ = 2

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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.