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

Example  2 - Chapter 13 Class 11 Limits and Derivatives - Part 3

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Example 2 Find the limits: (ii) (π‘™π‘–π‘š)┬(π‘₯β†’2) [(π‘₯^3 βˆ’ 4π‘₯^2 + 4π‘₯)/(π‘₯^2 βˆ’ 4)] (π‘™π‘–π‘š)┬(π‘₯β†’2) [(π‘₯^3 βˆ’ 4π‘₯^2 + 4π‘₯)/(π‘₯^2 βˆ’ 4)] = lim┬(xβ†’2) π‘₯(π‘₯^2 βˆ’ 4π‘₯ + 4)/(π‘₯^2 βˆ’γ€– (2)γ€—^2 ) = lim┬(xβ†’2) (π‘₯ (π‘₯^2 + 2^2 βˆ’ 4π‘₯ ))/((π‘₯ βˆ’ 2) (π‘₯ + 2)) = lim┬(xβ†’2) (π‘₯ (π‘₯ βˆ’ 2)^2)/((π‘₯ βˆ’ 2) (π‘₯ + 2)) = (π’π’Šπ’Ž)┬(π’™β†’πŸ) 𝒙(𝒙 βˆ’ 𝟐)/(𝒙 + 𝟐) Putting x = 2 = (2 (2 βˆ’ 2))/(2 + 2) = (2 (0))/4 = 0/4 = 0

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.