a) Find the function's domain . b) Find the function's range. c) Find the boundary of the function's domain. d) Determine if the domain is an open region, a closed region , or neither. e) Decide if the domain is bounded or unbounded. for: f(x,y) = 1/((16- x^2 -y^2)^(1/2))

Rivka Thorpe 2020-11-02 Answered
a) Find the functions
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Arham Warner
Answered 2020-11-03 Author has 102 answers

a)Determine the domain of the multivariable function.
Also, 16x2y2>0
From, x2+y216andx2+y2<16
The domain for f(x,y) is (x,y) R2:x2+y2<16.
b) Evaluate the range for the given function.
Range for 16x2y2is(0,16].
Therefore, range for f(x,y) is
As 16x2y20,f(x,y)
As 16x2y216,f(x,y)14
Therefore, range for f(x,y)[14,).
c)Determine the boundary of the domain using the domain for f(x, y).
The domain for f(x,y) is (x,y) R2:x2+y2<16.
The equation x2+y2<16 is a circle.
The boundary for the domain is points lying in the circle x2+y2=16.
d) The domain for the function f(x, y) do not contain the boundary points. Therefore, the domain for the function is an open region.
e) The domain for the function is enclosed in the circle.
Hence, the domain is bounded in the circle of equation x2+y2<16.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-08
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
asked 2021-11-23
The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
c. What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?
asked 2021-11-16
Stock analysis. The price-earning ratios of 100 randomly selected stocks from the New York Stock
a. Find the mean of the price-earning ratios.
asked 2021-09-19
Find the Jacobian of the transformation
asked 2021-11-18
Why is it very easy to conclude that 1x2dx diverges without making any integration calculations?
asked 2022-05-02

use squeeze theorem find the following lim x,y-0,0 y^2(1-cos2x) /x^4 +y^2