Vector Functions
Vector-Valued Function:
A vector-valued function F of a real variable with domain D assigns to each number t in the set D a unique vector F(t). The set of all vectors v of the form v =F(t) for t in D is the range of F. In three dimensions vector function can be expressed in the form
are real-valued functions of real variable t where
defined on the domain set D. A vector function may also be denoted by
Unless stated otherwise, the domain of a vector function is the intersection of the domains of the component functions
Remark:
The vector function
is called the particle s position vector when
Example: (Evaluate a vector function)
If
Then the component functions are:
and
. where
Limits and Continuity of a Vector Function:
Limits of a Vector Function:
is a vector and F is a vector-valued If
defined by the rule function of t
if then F has limit L as t approaches
and
Example:
then If
Continuity of a Vector Function:
if The vector function F is continuous at a point
It is continuous if it is continuous at every point in its domain.
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