Homework Answers
Add Answer to:
Log(2 - 2) Consider the function f(x, y,z) (a) What is the maximal domain off? (Write your answer...
Log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Question 3. Consider the function h: R3 → R h(x, y, 2) = (x2 + y2...
Question 3. Consider the function h: R3 → R h(x, y, 2) = (x2 + y2 + 2) +3/(x2 + 2xy + y) (a) What is the maximal domain of h? Describe it in words. (it may help to factor the denominator in the second term) > 0 for any a, (b) It is difficult to immediately find the range of h. Using the fact that a show that h cannot take negative values. Can h be an onto function?...
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 =...
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 = 9 (i) Find Vf(x,y,z). [3 marks] (ii) Verify that (2,1,0) is a point on this surface. Find the cartesian equation of the tangent plane to this surface at the point (2.1,0). [5 marks]
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves f...
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface.
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Det...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the max...
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x,...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Question 3. Consider the function h: R3 → R h(x, y, 2) = (x2 + y2 + 2) +3/(x2 + 2xy + y) (a) What is the maximal domain of h? Describe it in words. (it may help to factor the denominator in the second term) > 0 for any a, (b) It is difficult to immediately find the range of h. Using the fact that a show that h cannot take negative values. Can h be an onto function?...
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 = 9 (i) Find Vf(x,y,z). [3 marks] (ii) Verify that (2,1,0) is a point on this surface. Find the cartesian equation of the tangent plane to this surface at the point (2.1,0). [5 marks]
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface.
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
Most questions answered within 3 hours.
-
Name the following coordination compounds using systematic
nomenclature.
1. [Co(H2O)6]Cl2:
2. [Cr(NH3)6](NO3)3:
3. K4[Fe(CN)6]:
4. Na[Au(CN)4]:...
asked 6 minutes ago -
This assignment will explore the impact of corporate decisions
on a local versus a global perspective....
asked 1 hour ago -
Given the function below, F(w,x,y,z)= x’z+w’z’+w’y
a) draw a logic diagram for an implementation which uses...
asked 53 minutes ago -
The sandwich maker of the EE-Cole-Eye Sandwich Truck was just
fired (for a reason described below)...
asked 31 minutes ago -
Most political philosophers believe we have a duty to obey laws,
even if the laws in...
asked 1 hour ago -
Which of the following are common negotiation outcome
mistakes?
a. Leave money on the table b....
asked 2 hours ago -
Propose an efficient synthesis of 2-Bromo-5-nitrotoluene from
benzene. Hint: 3 steps. Consider directing effects of substituents....
asked 2 hours ago -
Convert the following quantities:
a) 0.819 atm to torr b) 512 mmHg to bar c) 11.2...
asked 2 hours ago -
C ++ Implement cat command
The purpose of this assignment is to provide practice using the...
asked 2 hours ago -
we
convert sugars into another form of stored potential energy. This
is called?
asked 3 hours ago -
The manufacturers of Oriental Spice Sauce are concerned that the
sodium levels in their product vary...
asked 3 hours ago -
PLEASE DON'T ANSWER IF YOU CAN'T ANSWER ALL OF THE QUESTIONS. I
DESPERATELY NEED HELP
Consider...
asked 3 hours ago