test2review_sp10-1

test2review_sp10-1 - MAT 267 TEST 2 REVIEW NOTE: Below the...

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MAT 267 TEST 2 REVIEW NOTE: Below the Examples and hw refer to examples and homework from the textbook, ww refers to webwork hw problems. CHAPTER 11 11.1 Know how to: Sketch the graph of basic surfaces (Examples 3,4, hw 18). Find the domain of two and three variable functions (Examples 1,2,10, ww 1, 2, hw 4, 8 ). Know how to graph level curves (Examples 6, 7, 8, 9, ww 6) and be able to match graphs of 3 dimensional surfaces and their contour maps (ww 4,5, hw 21, 22). Know how to find equations for the level surfaces of a three variable function (Example 11) . 11.3 Know how to Find partial derivatives of two and three variable functions algebraically (Examples 1, 3,5, ww 1-8), and how to estimate their value given the contour plot of the function (hw 2). Understand the geometrical meaning of the partial derivative with respect to x (rate of change in the direction of the positive x -axis) and y (rate of change in the direction of the positive y -axis) (Example 2, hw 2,3,4). Find higher order partial derivatives (Examples 6 and 7, ww 7, 8). Differentiate implicitly if z is defined implicitly as a function of x and y (Example 4, ww 9). (Note that in section 11.5 a very convenient formula for implicit differentiation is derived). 11.4 Be able to Find the equation of the tangent plane to a surface z = f ( x , y ) at a given point P 0 = x 0 , y 0 , z 0 : z = z 0 f x x 0 , y 0  x x 0  f y x 0 , y 0  y y 0 (Example 1, ww 1, 2) Find linear approximation (local linearization) of a two variable function f ( x , y ) at a given point x 0, y 0 : L x , y = f x 0,
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This note was uploaded on 08/25/2011 for the course CHE 113 taught by Professor Burrows during the Spring '11 term at ASU.

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test2review_sp10-1 - MAT 267 TEST 2 REVIEW NOTE: Below the...

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