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Find the unit tangent, principle unit normal, and binormal vectors of the described curve. Give answers in simplest form.  r(t) =

Write the equation of the line that is normal to the plane 4x – y + 3z = 19 and passes through the point (5, 3, -1). 

Match the equation with the surface it defines. identify the surface by type (paraboloid, ellipsoid, etc.) Equation:    3×2 + 3y2 + 3z2 = 36 Which graph? [1] Choice A Choice B Choice C   What is the name of the graph?  [2]

Write the equation of the plane that contains the points P(0, 0, 0), Q(1, 2, 3), and R(2, 1, [a]).  Write your final answer in the form ax + by + cz = d.     

To the nearest degree, find the angle between the vectors: v = -i + 3j + [a]k w = 2i + [b]j + 4k

Part One: Material from Exam #1 For multiple choice, T/F, and fill in the blank questions, please answer accordingly. For free response, please work your problem on your scratch paper.     

If an converges to 0, then 

Part Four: Material from Exam #4 For multiple choice, T/F, and fill in the blank questions, please answer accordingly. For free response, please work your problem on your scratch paper. 

If an does not converge to 0, then 

Determine the interval of x-values for which the series converges: