![Brainly264](/avatars/43243.jpg)
Brainly264
21.11.2019 •
Mathematics
Let φ(x, y) = arctan (y/x) .
(a) find the vector field f : = ∇φ, and simplify its components as much as possible.
(b) what is the domain of definition of f?
(c) find all the points (a, b) (belonging to the domain of definition of f) at which the vector f(a, b) is parallel to the line y = x. (note: for a real number u, arctan u is also denoted by tan−1 u. use the notation that you prefer.)
Solved
Show answers
More tips
- O Other What is the oldest joke ever told?...
- F Food and Cooking How to Make Lazy Cabbage Rolls? Simple Steps to a Delicious Dish...
- F Food and Cooking Unusually Delicious Shashlik - Follow the Etiquette of Proper Preparation!...
- L Leisure and Entertainment Couchsurfing: A New Way to Travel...
- G Goods and services Which TV is better - LCD or Plasma?...
- S Sport How to Learn to Pull Up on Monkey Bars?...
- L Leisure and Entertainment Scrapbooking: What is it and Why is it Becoming More Popular?...
- C Computers and Internet Where did torrents.ru move to?...
- B Business and Finance Understanding Cash Flow: What It Is and How It Works...
- C Computers and Internet What Are Peers and Seeds in Torrenting?...
Answers on questions: Mathematics
- M Mathematics Make a table of ordered pairs for the equation. y=1/2x−3 Then plot two points to graph the equation....
- M Mathematics What do you call a flying jew...
- M Mathematics Olve.make suremrs. cain s coleslaw recipe calls for cup of oil, 1 cup ofin each ratvinegar, and cup of sugar. tell whether each statementthe correcis true or false.a....
- H History Reasoning for declaring independence at this point in time....
- M Mathematics If 4x+7=18 what is the value of 12x+21show step by step work please...
Ответ:
a)![\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})](/tpl/images/0383/8589/bc392.png)
b)![\large \mathbb{R}^2-\{(0,0)\}](/tpl/images/0383/8589/73425.png)
c) the points of the form (x, -x) for x≠0
Step-by-step explanation:
a)
If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be
On one hand we have,
On the other hand,
So
b)
The domain of definition of F is
i.e., all the plane X-Y except the (0,0)
c)
Here we want to find all the points such that
where k is a real number other than 0.
But this means
So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0
Ответ:
help
plz
Step-by-step explanation: