Ex 13.2, 2 - Find derivative of 99x at x = 100 - Class 11 - Ex 13.2

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  1. Chapter 13 Class 11 Limits and Derivatives
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Ex 13.2, 2 Find the derivative of 99x at x = 100. Let f (x) = 99x We need to find derivative of f(x) at x = 100 i.e. f’ (100) We know that f’ (x) = lim﷮h→0﷯﷮ f x + h﷯−f (x)﷮h﷯﷯ Now, f(x) = 99 x So, f(x + h) = 99 (x + h) Putting values f’ (x) = lim﷮h→0﷯﷮ 99 𝑥 + ℎ﷯ − 99𝑥﷮h﷯﷯ = lim﷮h→0﷯﷮ 99𝑥 + 99 ℎ − 99𝑥﷮ℎ﷯﷯ = lim﷮h→0﷯﷮ 99ℎ﷮ℎ﷯﷯ = lim﷮h→0﷯ 99 = 99 Thus f’ (x) = 99 Putting x = 100 f’(100) = 99 Hence f’ (100) = 99

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