{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

32B(W08)_PracticeMidterm2

32B(W08)_PracticeMidterm2 - Z C xydx e y dy where C is the...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 32B - Lecture 4 - Winter 2008 Practice Midterm 2 - March 3, 2008 NAME: STUDENT ID #: DISCUSSION SECTION: This is a closed-book and closed-note examination. Calculators are not allowed. Please show all your work. Use only the paper provided. You may write on the back if you need more space, but clearly indicate this on the front. There are 6 problems for a total of 100 points. 1
Background image of page 1

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

View Full Document Right Arrow Icon
2 1.(15 points) Evaluate the line integral Z C 2 xye x 2 dx + e x 2 dy over a path C from (0,1) to (1,3).
Background image of page 2
3 2.(15 points) Find the work done by the force field F ( x, y, z ) = y i - x j + 2 z k in moving the particle along the arc of the circular helix r ( t ) = cos t i + sin t j + t k from the point (1 , 0 , 0) to the point (0 , 1 , π 2 )
Background image of page 3

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

View Full Document Right Arrow Icon
4 3.(15 points) Use Green’s Theorem to evaluate the line integral
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 Document Right Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Z C xydx + e y dy where C is the path from (0 , 0) to (1 , 1) along the graph of y = x 2 and from (1 , 1) to (0 , 0) along the graph of y = √ x. 5 4.(20 points) Find the area of the part of the surface with parametric equations x = u + v, y = uv, z = u-v, u 2 + v 2 ≤ 2 6 5.(15 points) For F = xy i + ( y 2-x 2 ) j + x 2 z 2 k find curl F and div F . 7 6.(20 points) Suppose that f is a scalar function and F is a vector field on R 3 . Prove the identity curl( f F ) = f curl F + ∇ f × F assuming that the appropriate partial derivatives exist and are continuous....
View Full Document

{[ snackBarMessage ]}