Quiz (Vector Functions)

Show all work and justify each step.

(1) Describe the graph in words and sketch a graph by hand for the vector function



(2) Show that the vector function

        
            
lies on the cone Sketch the curve.

(3) Describe the graph in words and sketch a graph by hand for the vector function



(4) How many revolutions are made by the circular helix



in a vertical distance of

(5) Find the domain of the vector function where

  

        
and



(6) Find a vector function whose graph is the curve of intersection of the hemisphere and the parabolic cylinder

(7) Find a vector function whose graph is the line of intersection of the planes and

(8) Determine the component functions for the vector function given by



where and

(9)  Determine the function given by



where and

(10)  Determine a function that satisfies



where and

(11)  Find the limit of the following vector-valued function, if it exists:



(12) Find the limit of the following vector-valued function, if it exists:



(13)  Find the limit of the following vector-valued function, if it exists:



(14) Determine so that



(15) Find a vector function such that is continuous at but is not continuous at

(16) Determine the intervals for which the vector functions and are continuous.

(17) Show that if is a vector function that is continuous at then is continuous at   

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