Maths Crash Course - Live lectures + all videos + Real time Doubt solving!

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 May 29, 2018 by Teachoo

Maths Crash Course - Live lectures + all videos + Real time Doubt solving!

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