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

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(C) Let $y = f(x) = x^{3000}$.We use the differential approximation formula: $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.Here,let $x = 1$ and $\De

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$1.6$

Vedclass · Answer

(C) Let $y = f(x) = x^{3000}$.We use the differential approximation formula: $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.Here,let $x = 1$ and $\Delta x = 0.0002$.Then $f(x) = 1^{3000} = 1$.The derivative is $f'(x) = 3000 x^{2999}$.At $x = 1$,$f'(1) = 3000(1)^{2999} = 3000$.Now,calculate the change $\Delta y \approx f'(x) \Delta x = 3000 	imes 0.0002 = 0.6$.Therefore,$f(1.0002) \approx f(1) + \Delta y = 1 + 0.6 = 1.6$.

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

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