Example 3 - Chapter 13 Class 11 Limits and Derivatives - Part 5

Example 3 - Chapter 13 Class 11 Limits and Derivatives - Part 6
Example 3 - Chapter 13 Class 11 Limits and Derivatives - Part 7

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Transcript

Example 3 Evaluate: (ii) (𝑙𝑖𝑚)┬(𝑥→0) (√(1 + 𝑥) − 1)/𝑥 (𝑙𝑖𝑚)┬(𝑥→0) (√(1 + x )− 1)/x Putting x = 0 = (√(1 + 0) − 1)/0 = (√(1 ) − 1)/0 = (1 − 1)/0 = 0/0 Since it is a 0/0 form We simplify the equation Putting y = 1 + x ⇒ y – 1 = x As x → 0 y → 1 + 0 y → 1 So, our equation becomes (𝑙𝑖𝑚)┬(𝑥→0) (√(1 + 𝑥 )− 1)/𝑥 = (𝑙𝑖𝑚)┬(𝑦→1) (√𝑦 − 1)/(𝑦 − 1) = (𝑙𝑖𝑚)┬(𝑥→1) ( 𝑦^((−1)/2) − 1)/(𝑦 − 1) = (𝑙𝑖𝑚)┬(𝑥→1) ( 𝑦^((−1)/2) − 1^((−1)/2))/(𝑦 − 1) = 1/2 × 1^((−1)/2 − 1) = 1/2 × 1 = 𝟏/𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.