# Example 19 (ii) - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)

Last updated at Aug. 28, 2021 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

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) You are here

Example 20 (i)

Example 20 (ii) Important

Example 21 (i)

Example 21 (ii) Important

Example 22 (i)

Example 22 (ii) Important

Last updated at Aug. 28, 2021 by Teachoo

Example 19 Find the derivative of f from the first principle, where f is given by (ii) f(x) = x + 1/x Given f (x) = x + 1/x We need to find Derivative of f(x) i.e. f’ (x) We know that f’(x) = lim┬(h→0) 𝑓〖(𝑥 + ℎ) − 𝑓(𝑥)〗/ℎ Here, f(x) = x + 1/x f(x + h) = (x + h) + 1/(x + ℎ) Putting values f’(x) = lim┬(h→0)〖(((𝑥 + ℎ)+ 1/(𝑥 + ℎ)) − (𝑥 + 1/𝑥))/h〗 = lim┬(h→0)〖(𝑥 + ℎ+ 1/(𝑥 + ℎ) − 𝑥 − 1/(𝑥 ))/h〗 = lim┬(h→0)〖(ℎ+ 1/(𝑥 + ℎ) − 1/𝑥 + 𝑥 − 𝑥)/ℎ〗 = lim┬(h→0)〖(ℎ+ 1/(𝑥 + ℎ) − 1/𝑥)/ℎ〗 = lim┬(h→0)〖(ℎ+ (𝑥 − (𝑥 − ℎ))/((𝑥 + ℎ) (𝑥)))/ℎ〗 = lim┬(h→0)〖(ℎ + ((−ℎ))/((𝑥 + ℎ) 𝑥))/ℎ〗 = lim┬(h→0)〖( ℎ(1 − 1/((𝑥 + ℎ) 𝑥)))/ℎ〗 = lim┬(h→0)(1−1/((𝑥 + ℎ) 𝑥)) Putting h = 0 = [1−1/(𝑥 (𝑥 + 0) )] = 𝟏−𝟏/(𝒙𝟐 )