Example 14 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
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
Examples (Term 1 and Term 2)
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
Examples (Term 1 and Term 2)
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