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In this video I prove the main properties of vector function limits, namely the addition, constant multiplication, as well as the dot and cross products of their limits. These properties are identical to the corresponding limits for real-valued functions. In each case we use the definition of a vector function limit to go from one side of the equation to the other. The limit of the addition, dot product, or cross product of two vector functions is the same as the corresponding limit for each vector function separately. And a constant inside a vector function limit can be factored out just as in real-valued functions.
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Timestamps
Exercise 2: Properties of Vector Function Limits: 0:00
Solution: Define the vector functions in 3D and use Definition 1: 1:17
Solution to (a): Addition of vector function limits: 2:34
Applying Definition 1: 11:00
Solution to (b): Constant multiplied by a vector function limit: 11:53
Reverse direction of Definition 1: 15:08
Solution to (c): Dot product of vector function limits: 16:08
Factor out the limit: 21:24
Solution to (d): Cross product of vector function limits: 22:44
Reverse direction of Definition 1: 32:17
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