Example 2 (iii) - Chapter 12 Class 11 Limits and Derivatives

Last updated at Dec. 16, 2024 by

Example 2 - Chapter 13 Class 11 Limits and Derivatives - Part 4 Example 2 - Chapter 13 Class 11 Limits and Derivatives - Part 5

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Example 2 Find the limits: (iii) lim┬(x→2) [(x2 −4)/(x3 − 4x2 + 4x)] lim┬(x→2) [(x2 − 4)/(x3− 4x2 + 4x)] = lim┬(x→2) [(x2 −(2)2)/(x(x2 − 4x + 4) )] = lim┬(x→2) [((𝑥 − 2) (𝑥 + 2))/(x(x(x − 2) − 2(x − 2)) )] = lim┬(x→2) [((𝑥 − 2) (𝑥 + 2))/(𝑥 (x − 2)(x − 2) )] = (𝐥𝐢𝐦)┬(𝐱→𝟐) [(𝒙 + 𝟐)/(𝐱 (𝐱 − 𝟐) )] Putting x = 2 = (2 + 2)/(2 (2 − 2) ) = (2 + 2)/(2 (2 − 2) ) = 4/(2(0)) = 𝟒/𝟎 = ∞ Which is not defined

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