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Ex 12.2, 5 - Chapter 12 Class 11 Limits and Derivatives
Last updated at May 29, 2023 by Teachoo
Ex 12.2
Ex 12.2, 1
Ex 12.2, 2
Ex 12.2, 3
Ex 12.2, 4 (i) Important
Ex 12.2, 4 (ii)
Ex 12.2, 4 (iii) Important
Ex 12.2, 4 (iv)
Ex 12.2, 5 You are here
Ex 12.2, 6
Ex 12.2, 7 (i) Important
Ex 12.2, 7 (ii)
Ex 12.2, 7 (iii) Important
Ex 12.2, 8
Ex 12.2, 9 (i)
Ex 12.2, 9 (ii) Important
Ex 12.2, 9 (iii)
Ex 12.2, 9 (iv) Important
Ex 12.2, 9 (v)
Ex 12.2, 9 (vi)
Ex 12.2, 10 Important
Ex 12.2, 11 (i)
Ex 12.2, 11 (ii) Important
Ex 12.2, 11 (iii) Important
Ex 12.2, 11 (iv)
Ex 12.2, 11 (v) Important
Ex 12.2, 11 (vi)
Ex 12.2, 11 (vii) Important
Transcript
Ex 12.2, 5 For the function f(x) = x100100 + x99100 +….+ x22 + x + 1. Prove that f’(1) = 100 f’(0) We have f (x) = 𝑥100100 + 𝑥9999 + …… + 𝑥22 + x + 1 f’ (x) = 1100 x100 + 199 x99 + …… + 12 x2 + x1 + 1′ f’ (x) = 1100 × 100x100 – 1 + 199 × 99x99 – 1 + … + 12 × 2x2 – 1 + 1.x1-1 + 0 = 100100 x99 + 9999 x98 + …+ 22 x1 + x0 + 0 = x99 + x98 + …..+ x + 1 + 0 = x99 + x98 + … + x + 1 Hence , f’ (x) = x99 + x98 + … + x + 1 We need to prove f’(1) = 100 f’(0) Hence R.H.S = L.H.S Hence proved
