Give an example of a function f(x, y) that is defined on R2 and has only...
Give an example of a function f(x, y) that is defined on R2 and has only hyperbolas as its level sets.
At the moment I have x2 - y2 = k (where k is a constant) as my answer. But I'm not sure if that is correct. It seems to work except when k = 0, which I'll have only two lines (y = x and y = -x) so I'm not too sure what should I do with it. Plus how should I explain that the function is what the question's asking for? What I've done so far was only sketch it when k = 1,2,3,-1,-2,-3 to show they are in the shapes of hyperbolas (and I didn't sketch k = 0 yet). Would that be enough or should I put more work?
Homework Answers
Add Answer to:
Give an example of a function f(x, y) that is defined on
R2 and has only...
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B...
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1}
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 -...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 - 1)(x + y - 4). (a) In three separate diagrams draw the level sets of the function at C=2, C = 4, and C= 6. State the coordinates of any isolated points and the radii of any circles that make up these level sets. (Hint: To get an idea of what the surface looks like it might help to look at the curves f(0,y)...
10. (10 points) A function f : R2 + R is called a probability density function...
10. (10 points) A function f : R2 + R is called a probability density function on D CR if (6) f(, y) 0 for all (x, y) E D and (i) SD. f(x,y)dA= 1. ſk(1 – 22 – y2) 22 + y2 <1 (a) For what constant k is the function f(z,y) a prob- 12 + y2 > 1 ability density function? Note that D= {(1, Y) ER? : x2 + y² <1}, the closed unit disk in R2...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
R.V. X and Y have the following joint density function: f(x, y) = { Cx2y, x2...
R.V. X and Y have the following joint density function: f(x, y) = { Cx2y, x2 ≤ y ≤ 1, 0, o.w. What is the constant C and E(Y |X = 1/2). For C I got 14 but I'm not sure that is correct.
Consider the function T: K3 K3 defined by T(x, y, z) = (0, y,0). This kind...
Consider the function T: K3 K3 defined by T(x, y, z) = (0, y,0). This kind of function is called a projection, since we are 'projecting' the vector (2, y, z) onto the y-axis. In this problem, you will prove that the function T is linear. In the first part, you will prove that T preserves addition. In the second part, you will prove that T preserves scalar multiplication. There is only one correct answer for each part, so be...
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 +...
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? ...
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? We can give a rigorous mathematical definition of a function. Most mathematicians don't use this on an everyday basis, but it is important to know that it exists and see it once in your life. Notice this is very closely related to the idea of the graph of a function. Definition 9. Let X and Y be sets. Let R-X × Y...
please show correct answer, thank you Find and sketch the domain of the function. f(x, y)...
please show correct answer, thank you
Find and sketch the domain of the function. f(x, y) = √y+√4x² - y2 у 0 0 4 X 0 2 0 Type here to search a i
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1}
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...
Consider the surface defined by 2 = f(x,y), where f(x, y) = (x + y2 - 1)(x + y - 4). (a) In three separate diagrams draw the level sets of the function at C=2, C = 4, and C= 6. State the coordinates of any isolated points and the radii of any circles that make up these level sets. (Hint: To get an idea of what the surface looks like it might help to look at the curves f(0,y)...
10. (10 points) A function f : R2 + R is called a probability density function on D CR if (6) f(, y) 0 for all (x, y) E D and (i) SD. f(x,y)dA= 1. ſk(1 – 22 – y2) 22 + y2 <1 (a) For what constant k is the function f(z,y) a prob- 12 + y2 > 1 ability density function? Note that D= {(1, Y) ER? : x2 + y² <1}, the closed unit disk in R2...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
Consider the function T: K3 K3 defined by T(x, y, z) = (0, y,0). This kind of function is called a projection, since we are 'projecting' the vector (2, y, z) onto the y-axis. In this problem, you will prove that the function T is linear. In the first part, you will prove that T preserves addition. In the second part, you will prove that T preserves scalar multiplication. There is only one correct answer for each part, so be...
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
The definition we gave for a function is a bit ambiguous. For example, what exactly is a "rule"? We can give a rigorous mathematical definition of a function. Most mathematicians don't use this on an everyday basis, but it is important to know that it exists and see it once in your life. Notice this is very closely related to the idea of the graph of a function. Definition 9. Let X and Y be sets. Let R-X × Y...
please show correct answer, thank you
Find and sketch the domain of the function. f(x, y) = √y+√4x² - y2 у 0 0 4 X 0 2 0 Type here to search a i
Most questions answered within 3 hours.
-
A simple random sample of size n=64 is obtained from a
population with a mean of...
asked 58 minutes ago -
(2 dimensions, 1 object, 2 accelerations)
1) A projectile is thrown with a wind. The wind...
asked 1 hour ago -
Brian makes $34,100 per year. How much can Brian expect to
contribute to FICA taxes in...
asked 2 hours ago -
To buy a new house you must borrow $155,000. To do this you take
out a...
asked 2 hours ago -
Spacely Sprockets is evaluating the construction of a new plant
on land the company purchased for...
asked 3 hours ago -
1. Consider a linear regression model of y on K regressors and
an intercept.
(i) Describe...
asked 3 hours ago -
Enter a balanced equation for the reaction between hydrochloric
acid and sodium sulfite.
Express your answer...
asked 3 hours ago -
Give a regular expression describing the language
{x | x ∈ Σ* and x does not...
asked 3 hours ago -
Masses of 1.0 kg, 2.0 kg, and 3.0 kg are each separately subject
to a net...
asked 3 hours ago -
The mode of philosophical argumentation and thought. How do
philosophers think and write? What is important...
asked 3 hours ago -
At the beginning of the unit, you were asked whether you thought
it was appropriate or...
asked 4 hours ago -
Calculate the grams of carbon in 9.32 x 10+23 molecules of
benzene (C6H6).
asked 4 hours ago