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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 ) , 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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