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  • Find the approximate value of f (2.01), where f (x) = 4 x ^ 2 + 5 x + 2.

2. Find the approximate value of f (2.01), where f (x) = 4x^2 + 5x + 2.

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Let x = 2 and \Delta x = 0.01
f(x+\Delta x) = 4(x+\Delta x)^2 +5(x+\Delta x)+2
\Delta y = f(x+\Delta x) - f(x)\\ f(x+\Delta x) = \Delta y + f(x)
We know that \Delta y is approximately equal to dy
dy = \frac{dy}{dx}.\Delta x\\ dy = (8x+5).(0.01) \ \ \ \ \ \ \ \ \ (\because y = f(x) = 4x^2+5x+2 \ and \ \Delta x = 0.01)\\ dy = 0.08x+0.05
f(x+\Delta x) = \Delta y + f(x)\\ f(x+\Delta x) = 0.08x + 0.05 + 4x^2 + 5x +2\\ f(x+\Delta x) = 0.08(2)+0.05+4(2)^2+5(2)+2\\ f(x+\Delta x) = 0.16 + 0.05 + 16 + 10 + 2\\ f(x+\Delta x) = 28.21
Hence, the approximate value of f (2.01), where f (x) = 4x^2 + 5x + 2. is 28.21

Posted by

Gautam harsolia

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