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Example 3 (ii) - 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 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
