Our first step in studying the calculus of vector-valued functions is to define what exactly a vector-valued function is. These definitions and theorems support the presentation of material in the rest of this chapter and also in the remaining chapters of the text. In this section we extend concepts from earlier chapters and also examine new ideas concerning curves in three-dimensional space. Our study of vector-valued functions combines ideas from our earlier examination of single-variable calculus with our description of vectors in three dimensions from the preceding chapter. 3.1.4 Define the limit of a vector-valued function.3.1.3 Describe the shape of a helix and write its equation.3.1.2 Recognize parametric equations for a space curve.3.1.1 Write the general equation of a vector-valued function in component form and unit-vector form.
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