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

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

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  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.