4.1 Class Notes - April 17 Prelim 3 a week from today...

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April 17Prelim 3 a week from today covers7.4 Definite integrals8.2 Volumes, 8.4 Improper Integrals8.1 Integration by partsCh. 11. Probability distributions9.2 Partial derivativesi.e., the material from HWK 7,8,9Formula and review sheets on BlackboadPartial DerivativesGiven ( , ) the partial derviative is computed by holdingconstant anddifferentiating the resulting function of f x yfxyxf(x,y) = – x2– y22Set 1( ,1)122yf xxfxxfyy= −== −= −Example x22Volume of a cone( , )3233r hV r hVrhrVrhπππ===Example221222222( ,)()2()1()0 ()1()()xf x yxxyxyfxxyxxxyfxyxxxyyxy==+++=++= −+=+Explaining f/y222222( ,)()3(3,)33(3)xf x yxyfxyxyfyyfyy=+= −+=+= −+
Problem 13 on page 517233232223( ,)ln(13)16131913f x yx yfxyxx yfx yyx y=+=+=+Problem 1722222( ,)2x yx yx yx yf x yxefexexyxfxexy==+=Higher order partials23223222222( ,)45128524152482430241548f x yxxyx yffxyxyxyx yxyffyxyxxxyyffyxyyxxy=+
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