Ex 12.2, 2 - Chapter 12 Class 11 Limits and Derivatives

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Ex 13.2, 2 - Find derivative of x at x = 1 - Class 11 Limits

Ex 13.2, 2 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Ex 12.2, 2 Find the derivative of x at x = 1. Let f (x) = x We need to find derivative of f(x) at x = 1 i.e. f’ (1) We know that f’ (x) = (π‘™π‘–π‘š)┬(β„Žβ†’0)⁑〖(𝑓(π‘₯ + β„Ž) βˆ’ 𝑓 (π‘₯))/β„Žγ€— Here, f(x) = x So, f(x + h) = x + h Putting values f’ (x) = lim┬(hβ†’0)⁑〖((π‘₯ + β„Ž) βˆ’ π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(π‘₯ + β„Ž βˆ’ π‘₯)/β„Žγ€— = lim┬(hβ†’0)β‘γ€–β„Ž/β„Žγ€— = lim┬(hβ†’0) 1 = 1 Hence, f’(x) = 1 Putting x = 1 f’(1) = 1 So, derivative of x at x = 1 is 1

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