The approximate value of (1.0002)^{3000} is | vedclass

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(C) Let $y = f(x) = x^{3000}$.We need to find the approximate value of $(1 + 0.0002)^{3000}$.Here,$x = 1$ and $\Delta x = 0.0002$.The formula for the

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$1.6$

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(C) Let $y = f(x) = x^{3000}$.We need to find the approximate value of $(1 + 0.0002)^{3000}$.Here,$x = 1$ and $\Delta x = 0.0002$.The formula for the differential is $\Delta y \approx dy = f'(x) \Delta x$.First,find the derivative: $f'(x) = 3000 x^{2999}$.Now,substitute the values: $dy = 3000(1)^{2999} 	imes 0.0002$.$dy = 3000 	imes 0.0002 = 0.6$.The approximate value is $f(x + \Delta x) \approx y + dy = 1^{3000} + 0.6 = 1 + 0.6 = 1.6$.

The approximate value of $(1.0002)^{3000}$ is

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