Example 4 (i) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1 (i)
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Transcript
Example, 4 Evaluate: (i) limx→0 sin4xsin 2x limx→0 sin4xsin 2x = limx→0 sin 4x × limx→0 1 sin2𝑥 Multiplying & dividing by 4x = limx→0 sin 4x . 4𝑥4𝑥 × limx→0 1 sin2𝑥 = limx→0 sin4𝑥4𝑥 . 4x × limx→0 1 sin2𝑥 = 𝐥𝐢𝐦𝐱→𝟎 𝒔𝒊𝒏𝟒𝒙𝟒𝒙 × limx→0 4x × limx→0 1 sin2𝑥 = 1 × limx→0 4x × limx→0 1 sin2𝑥 = 1 × limx→0 4x × limx→0 1 sin2𝑥 = limx→0 1 sin2𝑥 . 4x Multiplying & dividing by 2x = limx→0 1sin 2x × 4x × 2𝑥2𝑥 = limx→0 2𝑥sin 2x × 4𝑥2𝑥 = limx→0 2𝑥 sin2𝑥 × 2 = 2 limx→0 2𝑥 sin2𝑥 = 2 ÷ 𝐥𝐢𝐦𝐱→𝟎 𝐬𝐢𝐧𝟐𝒙𝟐𝒙 = 2 ÷ 1 = 21 = 2
