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This document provides a comprehensive overview of various mathematical expressions and functions commonly encountered in multivariable calculus. It covers operations involving summation, averaging, and the relationships between different variables, such as La, Lb, Lc, and others. The expressions are analyzed to understand their parameters and behavior, offering valuable insights for students and professionals in mathematics and engineering. The use of functional notation enhances clarity in conveying complex calculations, promoting a deeper understanding of multivariable functions.
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Table A-1 f(x) or g(x) e e e e e11e e e g e f e h L L L L L L L L L L Lae Lae/2 Lae/2 La(e+f)/2 La(g+h)/2 2Lae/3 2Lae/3 2Lae/3 Lae/3 Lae/3 a L Lae/2 Lae/3 Lae/6 La(2e+f)/6 La(h+2g)/6 Lae/3 Lae/4 5Lae/12 Lae/12 Lae/4 a L Lae/2 Lae/6 Lae/3 La(e+2f)/6 La(g+2h)/6 Lae/3 5Lae/12 Lae/4 Lae/4 Lae/12 a L Le(a+b)/2 Le(b+2a)/6 Le(a+2b)/6 Lb(e+2f)/6 + La(f+2e)/6 Lh(2b+a)/6 + Lg(b+2a)/6 L(a+b)e/3 L(3b+5a)e/12 L(5a+3b)e/12 L(a+3b)e/12 L(3a+b)e/12 a b L Le(c+d)/2 Le(2c+d)/6 Le(c+2d)/6 Lc(2e+f)/6 + Ld(e+2f)/6 Lh(c+2d)/6 + Lg(d+2c)/6 L(c+d)e/3 L(3c+5d)e/12 L(3c+5d)e/12 L(c+3d)e/12 L(3c+d)e/12 c d L
