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### Lecture5bc

Course: MTH MTH122, Spring 2009
School: SUNY Buffalo
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Word Count: 257

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to Math Welcome 122 Lecture 5 Survey of Calculus and its Applications I1 Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Chapter 7 Functions of Several Variables Last time Examples of Functions of Several Variables 7.2 Partial Derivatives Section Outline Partial Derivatives Computing Partial Derivatives Evaluating Partial Derivatives at a Point Local Approximation of f (x, y) Demand...

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to Math Welcome 122 Lecture 5 Survey of Calculus and its Applications I1 Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Chapter 7 Functions of Several Variables Last time Examples of Functions of Several Variables 7.2 Partial Derivatives Section Outline Partial Derivatives Computing Partial Derivatives Evaluating Partial Derivatives at a Point Local Approximation of f (x, y) Demand Equations Second Partial Derivative Partial Derivatives Definition Example Partial Derivative of f (x, y) If f ( x, y ) = 2 x 3 y 4, then with respect to x: written f , f x = and the derivative of f (x, y), x where y is treated as a constant and f (x, y) is f = considered as a function of x y alone Computing Partial Derivatives EXAMPLE Compute SOLUTION f for f f ( x, y ) = x 2 e 3 x ln y. and x y Computing Partial Derivatives EXAMPLE Compute f L for f (L, K ) = 3 LK . SOLUTION Evaluating Partial Derivatives at a Point EXAMPLE Let f (x, y, z ) = xy 2 z + 5. Evaluate f at (x, y, z) = (2, -1, 3). y SOLUTION Local Approximation of f (x, y) Local Approximation of f (x, y) EXAMPLE Let f (x, y, z ) = xy 2 z + 5. Interpret the result SOLUTION f (2,1,3) = 12. y Demand Equations EXAMPLE The demand for a certain gas-guzzling car is given by f (p1, p2), where p1 is the price of the car and p2 is the price of gasoline. Explain why f < 0. p2 f < 0 and p1 SOLUTION Second Partial Derivative EXAMPLE Le f (x, y ) = xe y + x 4 y + . 3. Find y SOLUTION 2 f . xy
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SUNY Buffalo - MTH - MTH122
Welcome toMath 122 Lecture 6 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Last timePartial derivativesDefinition ExamplePartial Derivative of f (x, y) If f ( x, y ) = 2 x
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Welcome toMath 122 Lecture 7 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Last timeFinding Relative Maxima and Minima 7.4Lagrange Multipliers and Constrained Optimizatio
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Welcome toMath 122 Lecture 8 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! ! !Partial Derivatives Finding Relative Maxima and Minima Lagrange Multipliers and Constrained O
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Welcome toMath 122 Lecture 9 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! ! !Functions of Several Variables Partial Derivatives Finding Relative Maxima and Minima Lagrang
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Welcome toMath 122 Lecture 10 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009!Integration by SubstitutionIf u = g(x), then 9.2Integration by Parts!Integration by Part
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Welcome toMath 122 Lecture 11 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! !Integration by Substitution Integration by Parts 9.3Evaluation of Definite Integrals!Th
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MATH 122 (Section C)Survey of Calculus &amp; its Applications 2Spring 2009TIME: INSTRUCTOR: OFFICE: PHONE: E-MAIL: WEB (course):Course HandoutMWF 10:00-10:50am Quanlei Fang 106 Mathematics Building 645-6284 x159 qfang2@buffalo.edu http:/www.acsu.
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