The approximate value of f(x)=3x^{2}+5x+3 at | vedclass

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(A) Given $f(x)=3x^{2}+5x+3$. We need to find the approximate value at $x=3.02$. Let $x = a + h$,where $a=3$ and $h=0.02$. The formula for linear appr

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$45.46$

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(A) Given $f(x)=3x^{2}+5x+3$. We need to find the approximate value at $x=3.02$. Let $x = a + h$,where $a=3$ and $h=0.02$. The formula for linear approximation is $f(a+h) \approx f(a) + h \cdot f^{\prime}(a)$. First,calculate $f(a) = f(3) = 3(3)^{2} + 5(3) + 3 = 27 + 15 + 3 = 45$. Next,find the derivative $f^{\prime}(x) = 6x + 5$. Then,$f^{\prime}(a) = f^{\prime}(3) = 6(3) + 5 = 18 + 5 = 23$. Now,substitute these values into the formula: $f(3.02) \approx 45 + (0.02)(23) = 45 + 0.46 = 45.46$.

The approximate value of $f(x)=3x^{2}+5x+3$ at $x=3.02$ is

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