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Domain of a Vector Function
There is a Vector function of a single variable in R2 and R3 have the form,
r→ (t) = {f (t), g(t)}
r→ (t) = {f (t) , g(t), h(t)}
correspondingly, where f (t) , g (t) and h (t) are known as the component functions.
The major idea that we want to discuss in this part is that of graphing and identifying the graph specified by a vector function. Though, before we do that, we should talk briefly about the domain of a vector function. The domain of vector function is the set of all t's for that all the component functions are defined.
Arc Length with Vector Functions In this part we will recast an old formula into terms of vector functions. We wish to find out the length of a vector function, r → (t) =
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