MATH-275 Midterm: MATH 275 Boise State Exam3a short
15 Feb 2019
School
Department
Course
Professor
Math 275 - Summer 2016 - Final Exam A Name:
Part 1: Short Answer
•The first five (5) pages are short answer.
•Answers must use proper notation.
•Work is not required.
1. (8 points) Consider the vector field −→
F(x, y, z) = hyz, x, xyzi
(a) Find the divergence: div(−→
F) = −→
∇ · −→
F
(b) Find the curl: curl(−→
F) = −→
∇ × −→
F
2. (4 points) Match each integral from the bottom list with its application.
Write the Roman numeral of the correct integral in the blank.
Applications:
(a) The flux of a field through a surface:
(b) The mass of a wire:
(c) The work preformed by a field as an object moves along a path:
(d) The area of a surface:
Integrals:
I. ZC
δds
II. ZC
−→
F·d−→
s
III. ZZS
dS
IV. ZZS
−→
F·d−→
S
3. (4 points) Match each description with the correct infinitesimal element.
Write the Roman numeral of the correct element in the blank.
Description:
(a) The area of an infinitesimal parallelogram on a surface:
(b) A vector normal to a surface:
(c) An infinitesimal measure of length on a curve:
(d) A vector tangent to a curve.
Infinitesimal Elements:
I. ds
II. d−→
s
III. dS
IV. d−→
S
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