MTH 142 Chapter Notes - Chapter 13: Twisted Cubic, Trefoil Knot, Antiderivative
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Learning objectives: understanding vector functions and space curves, determining the continuity of vector functions. Any function whose domain is a set of real numbers and whose range is a set of vectors is known as a vector function or a vector valued function. A vector function is represented by following equation; where f(t), g(t) and h(t) are components of vector r(t). The limit of a vector function is defined by taking the limits of its component functions as shown below; If we want to find whether a vector function is continuous or not at a point a, we take its limit at that point and if the limit is equal to r(a) then the function is continuous. Suppose we have continuous real valued functions f, g and h on an interval i, then the set c of all points (x, y, z) in space is called a space curve when,
