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Chap13_Sec1

Chap13_Sec1 - VECTOR FUNCTIONS 13.1 Vector Functions and...

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13.1 Vector Functions nd Space Curves VECTOR FUNCTIONS and Space Curves In this section, we will learn about: Vector functions and drawing their corresponding space curves.

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VECTOR FUNCTION In general, a function is a rule that assigns to each element in the domain an element in the range. A vector-valued function, or vector function, is simply a function whose: s Domain is a set of real numbers. s Range is a set of vectors . We are most interested in vector functions r whose values are three- dimensional (3-D) vectors. This means that, for every number t in the domain of r , there is a unique vector in V 3 denoted by r ( t ). If f ( t ), g ( t ), and h ( t ) are the components of the vector r ( t ), then f , g , and h are real-valued functions called the component functions of r. We can write: r ( t ) = f ( t ), g ( t ), h ( t ) = f ( t ) i + g ( t ) j + h ( t ) k
LIMIT OF A VECTOR If r ( t ) = f ( t ), g ( t ), h ( t ) , then provided the limits of the component functions exist. If

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Chap13_Sec1 - VECTOR FUNCTIONS 13.1 Vector Functions and...

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