Homework Answers
Add Answer to:
Define f: R2R by 224V2 y) (0,0) 0 if (x, y)-(0,0) if (z, f(z, y) (a)...
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) =...
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) = (0,0). (i) Isf continuous at (0,0)? Justify your answer. (ii) Show that Daf(3,0) = x for all x and D.f(0,y) = -y for all y (iii) D2f(0,0) + D2,1f(0,0). (iv) Is f differentiable at (0,0)? Justify your answer.
8.) (minimum along lines does not mean minimum) Define f: R2 and, if (a, y)0, R by f(0,0) (a) Pro...
8.) (minimum along lines does not mean minimum) Define f: R2 and, if (a, y)0, R by f(0,0) (a) Prove that f is continuous at (0,0). Hint: show that 4r4y2 < (z4 + y2)2. (b) Let & be an arbitrary line through the origin. Prove that the restriction of f [0, π) and t E R. (c) Show that f does not have a local minimum at (0,0). Hint: consider f(1,12). to ( has a strict local minimum at (0,0)....
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0...
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f continuous at (0,0). 2. Compute the partial derivatives of f at any (x, y) E R2. Are the partial derivatives continuous (0,0). at (0,0) (0,0) and 3. Compute the second derivatives 4. Compute the linear approzimant of f at (0,0).
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the...
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
3. (1,7) (0,0) { 0 f (x, y) = 23r²ty (z,y) = (0,0) (a) (10 pts)...
3. (1,7) (0,0) { 0 f (x, y) = 23r²ty (z,y) = (0,0) (a) (10 pts) Evaluate the limit, or use a two-path test to show that it does not exist: lim f(x,y). (sy)(0,0) Math 250 Final Exam, CSU Northridge (b) (4 pts) Is f(x,y) continuous? Explain why or why not. 4. (17 pts) Use Lagrange multipliers to find the absolute maximum and absolute min- imum of f(x,y) = ry", subject to the constraint 3x² + y = 12. 5/12/20
2. Consider the function f : R2 → R defined below. r3уг_ if (x,y) (0,0) f(x,y)...
2. Consider the function f : R2 → R defined below. r3уг_ if (x,y) (0,0) f(x,y) = if (x, y) (0, 0) (a) Prove that f is continuous at (0,0) (b) Calculate the partial derivatives (0,0) and (0,0) directly from the definition of partial derivatives. (c) Prove that f is not differentiable at (0,0).
*Let f : R2 -R be given by z, y)(0,0 r, y)- 2y and f(0,0) =...
*Let f : R2 -R be given by z, y)(0,0 r, y)- 2y and f(0,0) = 0. (a) Decide if both partial derivatives of f exist at (0, 0) (b) Decide if f has directional derivatives along all v R2 and if so compute these. (c) Decide if f is Fréchet differentiable at (0, 0)? (d) What can you infer about the continuity of the partial derivatives at (0, 0)? て
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2 (b) At...
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2 (b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2
(b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a
2. Define f : RR by - y 1(x) = { "2+2 (ay) (0,0); (z,y) = (0,0). (i) Isf continuous at (0,0)? Justify your answer. (ii) Show that Daf(3,0) = x for all x and D.f(0,y) = -y for all y (iii) D2f(0,0) + D2,1f(0,0). (iv) Is f differentiable at (0,0)? Justify your answer.
8.) (minimum along lines does not mean minimum) Define f: R2 and, if (a, y)0, R by f(0,0) (a) Prove that f is continuous at (0,0). Hint: show that 4r4y2 < (z4 + y2)2. (b) Let & be an arbitrary line through the origin. Prove that the restriction of f [0, π) and t E R. (c) Show that f does not have a local minimum at (0,0). Hint: consider f(1,12). to ( has a strict local minimum at (0,0)....
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f continuous at (0,0). 2. Compute the partial derivatives of f at any (x, y) E R2. Are the partial derivatives continuous (0,0). at (0,0) (0,0) and 3. Compute the second derivatives 4. Compute the linear approzimant of f at (0,0).
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...
3. (1,7) (0,0) { 0 f (x, y) = 23r²ty (z,y) = (0,0) (a) (10 pts) Evaluate the limit, or use a two-path test to show that it does not exist: lim f(x,y). (sy)(0,0) Math 250 Final Exam, CSU Northridge (b) (4 pts) Is f(x,y) continuous? Explain why or why not. 4. (17 pts) Use Lagrange multipliers to find the absolute maximum and absolute min- imum of f(x,y) = ry", subject to the constraint 3x² + y = 12. 5/12/20
2. Consider the function f : R2 → R defined below. r3уг_ if (x,y) (0,0) f(x,y) = if (x, y) (0, 0) (a) Prove that f is continuous at (0,0) (b) Calculate the partial derivatives (0,0) and (0,0) directly from the definition of partial derivatives. (c) Prove that f is not differentiable at (0,0).
*Let f : R2 -R be given by z, y)(0,0 r, y)- 2y and f(0,0) = 0. (a) Decide if both partial derivatives of f exist at (0, 0) (b) Decide if f has directional derivatives along all v R2 and if so compute these. (c) Decide if f is Fréchet differentiable at (0, 0)? (d) What can you infer about the continuity of the partial derivatives at (0, 0)? て
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2 (b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2
(b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a
Most questions answered within 3 hours.
-
The factor of incentive scheme fail is because of rewards
rupture relationships. Explains
(in 300 words)
asked 9 minutes ago -
Given an operating system that supports a one-to-one
relationship between user-level threads and kernel-level threads
and...
asked 14 minutes ago -
1-7. Identify the initiation, propagation, and termination steps
for the following accident report. Suggest ways to...
asked 16 minutes ago -
How many photons are produced in a laser pulse of .125 J at 523
nm
asked 18 minutes ago -
how did government respond to the crash of 1929 and
financial crisis of 2008. Please provide...
asked 16 minutes ago -
An electrochemical cell consists of a Pt|H+(aq,1.00
M)|H2(g) cathode connected to a
Pt|H+(aq)|H2(g) anode in which...
asked 20 minutes ago -
Approximately 3.9 x 106 kg of water falls 65 m over a waterfall
each second. (a)...
asked 22 minutes ago -
Python Assignment: Write a program that uses stacks to solve
postfix equations.Read the below in a...
asked 39 minutes ago -
Q45 What do you understand by standardized tool of research? [1
Mark]
asked 42 minutes ago -
For the movie my big fat greek wedding
1. Locate and describe three instances of non-verbal...
asked 48 minutes ago -
When a bank makes its loans, if it screens its borrowers it will
collect repayment revenue...
asked 47 minutes ago -
A customer has requested that Lewelling Corporation fill a
special order for 2,400 units of product...
asked 1 hour ago