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Physics 1 Problem Solutions 17

# Physics 1 Problem Solutions 17 - Chapt 1 Quantities Units...

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Chapt. 1 Quantities, Units, Conversions, Measurement, Significant Figures, and Uncertainties 13 sufficiently small ( x x 0 ). The smaller ( x x 0 ) is the less important the higher order terms. In physics (and other fields no doubt), one is often interested in the behavior near some important point x 0 , and so truncates the Taylor’s series to find an simple approximate expression for the neighborhood of x 0 . For example f ( x ) = f ( x 0 ) , 0th order or constant approximation; f ( x 0 ) + ( x x 0 ) f ( x 0 ) , 1st order or linear approximation; f ( x 0 ) + ( x x 0 ) f ( x 0 ) + ( x x 0 ) 2 2 f ′′ ( x 0 ) , 2nd order or quadratic approximation. The 0th order expansion, approximates the function as a constant which is the function value at x 0 ; the 1st order expansion approximates the function by a line that is tangent to the function at x 0 ; the 2nd order expansion approximates the function by a quadratic that is tangent to the
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