# Example 14 - 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

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 You are here

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 14 Find the derivative of f(x) = 1 + x + x2 + x3 +... + x50 at x = 1. We need to find f’ (x) at x = 1 i.e. f’ (1) f(x) = 1 + x + x2 + x3 +………. + x50 f’(x) = 1 + x + x2 + x3 +………. + x50′ f’(x) = 0 + 1. x1-1 + 2x2-1 + 3x3-1 +………. + 50x50-1 = 1+ 2x + 3x2 +………. + 50x49 Hence , f’ (x) = 1 + 2x + 3x2 + … + 50x49 f’ (x) = 1 + 2x + 3x2 + … + 50x49 At x = 1 Putting x = 1 in f’(x) f’ (1) = 1 + 2 (1) + 3 (1)2 + ….. + 50 (1)49 = 1 + 2 + 3 +….. + 50 = 𝟓𝟎 (𝟓𝟎 + 𝟏)𝟐 = 50 (51)2 = 25 × 51 = 1275 Hence, f’(x) at x = 1 is 1275