Example 2 (iii) - Chapter 12 Class 11 Limits and Derivatives
Last updated at August 14, 2026 by Teachoo
Examples
Example 1 (i)
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Transcript
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
