The approximate value of 3^{2.001},given that | vedclass

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(D) Let $f(x) = 3^x$. Then,the derivative is $f'(x) = 3^x \log 3$. We need to find the value of $f(2.001)$. Here,$a = 2$ and $h = 0.001$. Using the li

Vedclass · Accepted Answer

$9.00989$

Vedclass · Answer

(D) Let $f(x) = 3^x$. Then,the derivative is $f'(x) = 3^x \log 3$. We need to find the value of $f(2.001)$. Here,$a = 2$ and $h = 0.001$. Using the linear approximation formula $f(a+h) \approx f(a) + h f'(a)$: $f(2.001) \approx f(2) + (0.001) f'(2)$. Substituting the values: $f(2.001) \approx 3^2 + (0.001)(3^2 \log 3)$. Given $\log 3 = 1.0986$: $f(2.001) \approx 9 + (0.001)(9 	imes 1.0986)$. $f(2.001) \approx 9 + (0.001)(9.8874)$. $f(2.001) \approx 9 + 0.0098874$. Rounding to the given options,we get $9.00989$.

The approximate value of $3^{2.001}$,given that $\log 3 = 1.0986$,is

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