Examples

Chapter 13 Class 11 Limits and Derivatives
Serial order wise

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### 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.