Example 19 (ii) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 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 )
Examples
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
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Example 8
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Example 11
Example 12
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Example 16
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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
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo