# Example 3 (ii) - Chapter 12 Class 11 Limits and Derivatives

Last updated at April 16, 2024 by Teachoo

Examples

Example 1 (i)

Example 1 (ii)

Example 1 (iii)

Example 2 (i)

Example 2 (ii) Important

Example 2 (iii) Important

Example 2 (iv)

Example 2 (v)

Example 3 (i) Important

Example 3 (ii) Important You are here

Example 4 (i)

Example 4 (ii) Important

Example 5

Example 6

Example 7 Important

Example 8

Example 9

Example 10 Important

Example 11

Example 12

Example 13 Important

Example 14

Example 15 Important

Example 16

Example 17 Important

Example 18

Example 19 (i) Important

Example 19 (ii)

Example 20 (i)

Example 20 (ii) Important

Example 21 (i)

Example 21 (ii) Important

Example 22 (i)

Example 22 (ii) Important

Last updated at April 16, 2024 by Teachoo

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