The derivative of the function f is defined by f^(')(x)=x^(2)cos(3x-3). If f(1)=7, then use a calculator to find the value of f(5) to the nearest thousandth. Answer:

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The derivative of the function  f is defined by  f^(')(x)=x^(2)cos(3x-3). If  f(1)=7, then use a calculator to find the value of  f(5) to the nearest thousandth. Answer:

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Integrate f'(x) from 1 to 5: To find the value of f(5), we need to integrate the derivative f'(x) from x=1 to x=5 and then add the initial value f(1)=7.Calculate Antiderivative F(x): The integral of f'(x) from 1 to 5 is the antiderivative of f'(x) evaluated at 5 minus the antiderivative evaluated at 1. ∫(from 1 to 5) x^2cos(3x-3) dx = F(5) - F(1), where F(x) is the antiderivative of f'(x).Use Numerical Integration: To find the antiderivative F(x), we need to use integration by parts or a suitable substitution. However, this integral does not have an elementary antiderivative, so we will use numerical integration to approximate the value.Approximate Integral Value: Using a calculator or numerical integration software, we approximate the integral of x^2cos(3x-3) from 1 to 5. This step requires the use of technology and cannot be accurately done by hand.Calculate f(5): After calculating the integral, we find the approximate value (let's call this value 'I') and then add the initial condition f(1)=7 to get f(5). f(5) = I + f(1) = I + 7.Find f(5) Value: Assuming the calculator gave us the value of the integral as 'I' (to the nearest thousandth), we can now calculate f(5). f(5) = I + 7.Finalize Solution: Since we do not have an actual calculator or software output, we cannot provide the numerical value of the integral 'I' or the final value of f(5). To complete this problem, you would need to use a calculator or numerical integration software to find 'I' and then add 7 to find f(5).

The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{2} \cos (3 x-3)$ . If $f(1)=7$ , then use a calculator to find the value of $f(5)$ to the nearest thousandth. $\newline$ Answer:

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The derivative of the function f f f is defined by f′(x)=x2cos⁡(3x−3) f^{\prime}(x)=x^{2} \cos (3 x-3) f′(x)=x2cos(3x−3). If f(1)=7 f(1)=7 f(1)=7, then use a calculator to find the value of f(5) f(5) f(5) to the nearest thousandth.\newlineAnswer:

The derivative of the function $f$ is defined by $f^{\prime}(x)=x^{2} \cos (3 x-3)$ . If $f(1)=7$ , then use a calculator to find the value of $f(5)$ to the nearest thousandth. $\newline$ Answer: