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15.1 Intro Fns Several Variables

# 15.1 Intro Fns Several Variables - Functions of Several...

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Functions of Several Variables

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Functions of Several Variables We are leaving vector valued functions behind …
Functions of Several Variables Instead, we will study function of several variables:

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Functions of Several Variables Notice the difference . Vector-valued function r(t) = <x(t),y(t),z(t)> plug in a number t, get a vector
Functions of Several Variables Function of several variables

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Functions of Several Variables Example
Functions of Several Variables COMPARE: r(t) = <x(t),y(t),z(t)> plug in t and get a vector

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Functions of Several Variables n variables
Functions of Several Variables Example

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Functions of Several Variables Example Maximum height (in feet) attained by an object thrown in the air with initial velocity v ft/s, at an angle f .
Functions of Several Variables Example Maximum height (in feet) attained by an object thrown in the air with initial velocity v ft/s, at an angle f . H(88,f /4) = 85.6 feet

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Functions have domains Example
Functions have domains Example Defined only if xy > 0, so the domain of f(x,y) is the set D = { (x,y): xy > 0 }

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Graphs of Multivariable Functions Can we visualize functions of several variables?
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