Mock_Exam1

# Mock_Exam1 - -xy 2-x 2 yz what is the direction of the...

This preview shows pages 1–8. Sign up to view the full content.

Mock Exam 1 1

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

View Full Document
1. a).Find the equation of the plane through (5,1,-2) perpendicular to n = < 2 , 4 , 3 > . Then find the angle between this plane and the one with equation 3x-4y+7z=5. b).Find the equation of the plane throught the three points P 1 (1 , - 2 , 3) , P 2 (4 , 1 , - 2) and P 3 ( - 2 , - 3 , 0). 2
2. a).Find the curvature of the circular helix r ( t ) = a cos t i + a sin t j + ct k , a > 0 b).Find T , N , a T , a N for the curve above. 3

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

View Full Document
3. Show that f ( x, y ) = xe y + x 2 y is differentiable everywhere and calculate its gradient. Then find the equation z = T ( x, y ) of the tangent plane at (2,0). 4
4. If the temperature at any point in a homogeneous body is given by T

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -xy 2-x 2 yz , what is the direction of the greatest drop in temperature at the point (1,-1,2)? 5 5. Find the maximum and minimum values of f ( x, y, z ) = x + 2 y + 3 z on the ellipse that is the intersection of the cylinder x 2 + y 2 = 2 and the plane y + z = 1. 6 6. Find the directional derivative of f ( x, y ) = e-x cos y at (0 , π/ 3) in the direction toward the origin. 7 7. Find the equation of the tangent plane and the normal line to the surface x 2 + y 2 + 2 z 2 = 23 at (1,2,3). 8...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern