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On the Sum of Square Roots of Polynomials and Related Problems

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... That is, an equation can be multiplied or divided by the same nonzero real number without changing the solution of the equation. Example: Solve 2x + 7 = 19. Original equation 2x + 7 = 19 The solution is preserved when 7 is 2x + 7  7 = 19  7 subtracted from both sides. 2x = 12 Simplify both sides. ...
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... One drawback of the trapezoidal rule is that the error is related to the second derivative of the function. More complicated approximation formulas can improve the accuracy for curves - these include using (a) 2nd and (b) 3rd order polynomials. The formulas that result from taking the integrals unde ...
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... has cusp points in sections of its singularity surfaces in the joint space [12, 14]. The 4 analytic manipulators defined in the past (cases (i), (ii), (iii) and (v) recalled in the introduction) do not have any cusp points. This is because the polynomials involved in their forward kinematics cannot ...
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Quartic function

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