# sn5_1 - Math 2433 Week 5 Popper005 1 What is today A Monday...

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Math 2433 Week 5 Popper005 1. What is today? A. Monday B. Tuesday C. Wednesday D. Thursday E. Friday 2. Express the curvature in terms of t . a) b) c) d) 14.1 Examples of real-valued functions of two and three variables (read this section!!) Finding domain and range: 1. ( , ) f x y xy =

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2. 1 ( , ) f x y x y = - 3. 2 2 ( , ) 9 4 f x y x y = - - - 4. 2 2 ( , , ) z f x y z x y = -
5. Express each of the following as a function of three variables. a. The surface area of a box with no top whose sides have lengths x , y and z . b. The angle between the vectors i + j and x i + y j + z k . c. The volume of the parallelepiped whose sides are the vectors i , i + j , and x i + y j + z k .

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6. For 2 ( , ) 2 f x y xy y = + , form the difference quotients Then, assuming that x and y are fixed, calculate the limit as h 0. What is the connection between your results and derivatives? Popper005 3. Find the domain of the given function: a) {( x , y )| y < 5x 2 } b) {( x , y )| y > 5x 2 } c) {( x , y )| y 5x 2 } d) {( x , y )| y < 5x 2 } e) {( x , y )| y > 5x 2 }
14.2

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sn5_1 - Math 2433 Week 5 Popper005 1 What is today A Monday...

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