exam1_samp - r(0 = h 3 4 i find the position at a general...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Your Name Printed Clearly! Your Discussion Leader Name Discussion Period EXAM 1 SAMPLE BOYLAND CALCULUS 3 SPRING 10 1. (a) Find a vector perpendicular to the plane containing the points A = (1 , 0 , 0) , B = (2 , 0 , - 1) and C = (1 , 4 , 3). (b) Find the area of the triangle ABC . 2. (a) Find the vector and scalar projection of the vector 2 i +3 j + - 2 k onto the vector 3 i + - j +4 k . (b) Find the equation of the plane parallel to the plane x + 2 y + 5 z = 3 and passing through the point ( - 4 , 1 , 2). Page 1 of 3 Total points this page out of 20
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. (a) Sketch the surface, labeling at least 4 points. 9 x 2 + y 2 + 4 z 2 = 16 (b) Find the equation of the tangent plane to the surface z = sin( xy ) at the point (1 , π/ 4 , 2 / 2) 4. A particle has constant acceleration a ( t ) = h 1 , 0 , 2 i and initial velocity v (0) = h 1 , - 2 , 3 i and initial position
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r (0) = h , 3 , 4 i find the position at a general time t and when t = 1. Page 2 of 3 Total points this page out of 20 5. Assume r ( t ) = h t 3 , 5 , 2 t 2 i . (a) Find the arc length for 0 ≤ t ≤ 1 (b) Find the unit tangent vector T ( t ) for t > 0. (c) Find the curvature κ ( t ) at a general point t > 0. (d) Find the parametric equation of the tangent line to the curve when t = 1 6. Find the linear approximation of the function f ( x,y ) = (4 x 2 + y 2 ) 1 / 3 at (1 , 2) and use it to approximate f (1 . 05 , 1 . 95). You must give a computed numerical answer, a fraction is OK. Page 3 of 3 Total points this page out of 20...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern