224Ex2-formulas

224Ex2-formulas - MA 22400 EXAM 2 FORMULAS TRAPEZOIDAL RULE...

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MA 22400 – EXAM 2 FORMULAS TRAPEZOIDAL RULE Z b a f ( x ) dx Δ x 2 ± f ( x 1 )+2 f ( x 2 )+2 f ( x 3 )+ ··· +2 f ( x n )+ f ( x n +1 ) ² , where a = x 1 ,x 2 ,x 3 ,...,x n +1 = b subdivides [ a,b ]into n equal subintervals of length Δ x = b - a n . THE SECOND DERIVATIVE TEST Suppose f is a function of two variables x and y , and that all the second-order partial derivatives are continuous. Let D = f xx f yy - ( f xy ) 2 and suppose ( a,b ) is a critical point of
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