Derivatives And Integrals Of Vector Functions

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  1. The figure shows a curve C given by a vector function rt .

    1. Draw the vectors r4.5r4 , r4.2r4 , r4.5r40.5 , and r4.2r40.2 .
    2. Write expressions for r4 and the unit tangent vector T4 . Draw the vector T4 .

    2D vector function

  2. Make a large sketch of the curve described by the vector function rt=t2t,0t2 , and draw the vectors r1 , r1.1 , and r1.1r1 . Moreover, draw the vector r1 starting at 11 and compare it with the vector


    Explain why these vectors are similar.

  3. Let rt=1+costi+2+sintj and t=π6 , sketch the plane curve with the given vector equation, find rt , and sketch the position vector rt and the tangent vector rt for the given value of t .
  4. Find the derivative of the vector function

    rt=et2ij+ln1+3tk .

  5. Find the unit tangent vector Tt at the point where t=0 for the curve given by the equation

    rt=costi+3tj+2sin2tk .

  6. Find parametric equations for the tangent line to the curve


    at the point 021 .

    x=t , y=2+t , z=1+2t
  7. At what point do the curves




    intersect? Find the angle of intersection to the nearest degree.

    104 , the angle is approx. 54.74°
  8. Evaluate the integral


  9. Find rt if rt=ti+etj+tetk and r0=i+j+k .