final265sp2007sol

final265sp2007sol - Math 265 Final Exam 2007/04/30 Name...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 265 Name & Section: %PI e Final Exam 2007/04/30 Instructor: A 1113Jtj Answer each question completely. Show all work. No credit is allowed for mere answers with no work shown. Show the steps of calculations. State the reasons that justify conclusions. 1. (12 points) Show that the triangle with vertices P = (4,1,3), Q = (2,0,5) and R = (4,2,8) is a right triangle. Which vertex has the right angle? =.J[z-ry +(5-3)' = JJ* = 5-3 = ((q-~)-r+ ~14)5+(%-~\~ 3 Jrn =fi r- KP = S~Y-QI* ~1-2)'*~3-b); = jG? = JZL. 1% N ~p~~~+~ni'= @PP -Ih~~v.cq . 5u Q is he vrvh* dh thl: k~g~ ~MJ& dl 2. (12 points) Find the point(s) on the upper half of the ellipsoid 2x2 + y2 + 3a2 = 1 where the tangent plane is parallel to the plane 4x - 4y + 6z = 15.
Background image of page 1

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

View Full DocumentRight Arrow Icon
1 1 3. (14 points) Find all critical points of f (x, y) = - + xy + -. Indicate whether each such x Y point gives a local maximum or a local minimum, or whether it is a saddle point.
Background image of page 2
4. (12 points) Find the volume of the solid in the first octant bounded by the coordinate planes and the planes
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

final265sp2007sol - Math 265 Final Exam 2007/04/30 Name...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online