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study guide exam 2 mth

study guide exam 2 mth - Study Guide for the 2nd Exam...

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Study Guide for the 2nd Exam MTH241 Exam Date: 28th October 2011. In class Exam Covers Sections 14 . 1 14 . 8 You must know the followings 1. Domain of the function. 2. Limit and Continuity Prove or disprove the existance of limit. Do all the problems from the handout which I distributed in class 3. Partial Derivatives. Find f x , f y , f xx , f yy , f xy etc 4. Tangent plances and linearizations. Equation of the tangent plane of the curve z = f ( x, y ) at ( a, b ) is given by f x ( a, b )( x a ) + f y ( a, b )( y b ) ( z f ( a, b )) = 0 Linearization of f ( x, y ) = 0 around ( a, b ) is given by f x ( a, b )( x a ) + f y ( a, b )( y b ) ( z f ( a, b )) = 0. 5. Chain Rule. Must know z = f ( x, y ) , x = g ( t ) , y = h ( t ) dz dt = f x dx dt + f y dy dt z = f ( x, y ) , x = g ( s, t ) , y = h ( s, t ) dz ds = f x x s + f y y s dz dt = f x x t + f y y t Implicit Di ff erentiation: F ( x, y ) = 0 , y = f ( x ) dy dx = F x F y 6. Directional Derivatives, Gradiant, Maximum rate of change. Finding the equations of Tangent plane and Normal lines .
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