multivariable_19_Useful_Formulas_4up

multivariable_19_Useful_Formulas_4up - 478 Appendix B...

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B Useful Formulas Algebra Remember that the common algebraic operations have precedences relative to each other: for example, mulitplication and division take precedence over addition and subtraction, but are “tied” with each other. In the case of ties, work left to right. This means, for example, that 1 / 2 x means (1 / 2) x : do the division, then the multiplication in left to right order. It sometimes is a good idea to use more parentheses than strictly necessary, for clarity, but it is also a bad idea to use too many parentheses. Completing the square: x 2 + bx + c = ( x + b 2 ) 2 - b 2 4 + c . Quadratic formula: the roots of ax 2 + bx + c are - b ± b 2 - 4 ac 2 a . Exponent rules: a b · a c = a b + c a b a c = a b - c ( a b ) c = a bc a 1 /b = b a Geometry Circle: circumference = 2 πr , area = πr 2 . Sphere: vol = 4 πr 3 / 3, surface area = 4 πr 2 . 477 478 Appendix B Useful Formulas Cylinder: vol = πr 2 h , lateral area = 2 πrh , total surface area = 2 πrh + 2 πr
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