The approximate value of x^3-2x^2+3x+2 at x=2 | vedclass

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(A) Let $f(x) = x^3-2x^2+3x+2$. We need to find the approximate value at $x = 2.01$. Let $a = 2$ and $h = 0.01$,so $x = a+h = 2.01$. The derivative is

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$8.07$

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(A) Let $f(x) = x^3-2x^2+3x+2$. We need to find the approximate value at $x = 2.01$. Let $a = 2$ and $h = 0.01$,so $x = a+h = 2.01$. The derivative is $f'(x) = 3x^2-4x+3$. Calculating $f(a)$ at $a = 2$: $f(2) = (2)^3-2(2)^2+3(2)+2 = 8-8+6+2 = 8$. Calculating $f'(a)$ at $a = 2$: $f'(2) = 3(2)^2-4(2)+3 = 12-8+3 = 7$. Using the linear approximation formula $f(a+h) \approx f(a) + h \cdot f'(a)$: $f(2.01) \approx 8 + (0.01)(7) = 8 + 0.07 = 8.07$.

The approximate value of $x^3-2x^2+3x+2$ at $x=2.01$ is

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