Calc11_3 FuncOfTwoInd

# Calc11_3 FuncOfTwoInd - → y x z ( 29 2 2 , 100 z f x y x...

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Greg Kelly, Hanford High School, Richland, Washington

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The functions that we have studied this year have all been functions of one independent variable: eg: ( 29 ( 29 ( 29 2 sin f x x f x x = = In real life, functions often have more than one independent variable: eg: 1 Area of a triangle: 2 A bh = ( 29 1 , 2 f b h bh = ( 29 2 2 2 , , f x y z x y z = + + 2 2 2 w x y z = + +
Functions with two independent variables can be represented graphically. This is not easy to do by hand, and our calculators do not do a great job either. ( 29 2 2 , 100 z f x y x y = = - -

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y x z ( 29 2 2 , 100 z f x y x y = = - - 10 10 100 sketch of graph

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Unformatted text preview: → y x z ( 29 2 2 , 100 z f x y x y = =--x y 10 10 10 10 100 sketch of graph level curves Level curves are drawn by holding the z value constant (similar to contour lines on a topographic map.) → y x z ( 29 2 2 , 100 z f x y x y = =--10 10 100 sketch of graph Let’s look at the same graph plotted on the TI-89: First change the mode to 3D. Then go to the Y= screen and enter the equation. → By pressing the arrow keys, you can rotate this graph! π...
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## This note was uploaded on 02/16/2012 for the course CALCULUS 1103 taught by Professor Walmer during the Fall '11 term at Broward College.

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Calc11_3 FuncOfTwoInd - → y x z ( 29 2 2 , 100 z f x y x...

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