Ex 12.2, 3 - Chapter 12 Class 11 Limits and Derivatives

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Ex 12.2, 3 - Find derivative of 99x at x = 100 - Class 11 - Ex 12.2

part 2 - Ex 12.2, 3 - Ex 12.2 - Serial order wise - Chapter 12 Class 11 Limits and Derivatives

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Ex 12.2, 3 Find the derivative of 99x at x = 100 Let f (x) = x We need to find derivative of f(x) at x = 100 i.e. f’ (100) We know that f’ (x) = (π‘™π‘–π‘š)┬(β„Žβ†’0)⁑〖(𝑓(π‘₯ + β„Ž) βˆ’ 𝑓 (π‘₯))/β„Žγ€— Here, f(x) = 99x So, f(x + h) = 99(x + h) = 99x + 99h Putting values f’ (x) = lim┬(hβ†’0)⁑〖((99π‘₯ +99β„Ž) βˆ’ 99π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(99π‘₯ +99β„Ž βˆ’ 99π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖99β„Ž/β„Žγ€— = lim┬(hβ†’0) 99 = 99 Hence, f’(x) = 99 Putting x = 100 f’(100) = 99 So, derivative of 99x at x = 100 is 99

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