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2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a....
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0)...
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
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
Q1. Let z = f(x,y) -√4x² – 2y² Find (i). domain of f(x,y) (ii). range of...
Q1. Let z = f(x,y) -√4x² – 2y² Find (i). domain of f(x,y) (ii). range of f(x,y) (iii). f(1,1) (iv). The level curves of f(x,y) for k = 0,1,2 4x2y Q3. Let f(x,y) = x2+y2 if (x,y) = (0,0) 1 if (x,y) = (0,0) Find (i) lim limf(x,y) (x,y)-(0,0) (ii). Is f(x, y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
Given the function f(r.y) lim f(x, y) (ry)-+(0,0) a. Evaluate iii. Along the line y= r: i. Along the r-axis: iv. Alo...
Given the function f(r.y) lim f(x, y) (ry)-+(0,0) a. Evaluate iii. Along the line y= r: i. Along the r-axis: iv. Along y12 ii. Along the gy-axis: ,f(x, y) exist? If yes, find the limit. If no, explain why not. lim (a.)-(0,0) b. Does (0,0)? Why or why not? c. Is f continuous at d. The graphs below show the surface and contour plots of f (graphed using WolframAlpha). Explain how the graphs explain your answers to parts (a)-(c) above....
Q2. x+y (a). Let f(x,y) = x²+y²+1 Find (i). lim (x,y)-(1,1) f(x,y) (ii). lim f(x,y) (x,y)-(-1,1)...
Q2. x+y (a). Let f(x,y) = x²+y²+1 Find (i). lim (x,y)-(1,1) f(x,y) (ii). lim f(x,y) (x,y)-(-1,1) (iii). lim f(x,y) (x,y)-(1,-1) (iv). lim f(x,y) (x,y)-(0,0) ( 4x²y if (x, y) = (0,0) Q3. Let f(x,y) = x2 + y2 1 if (x,y) = (0,0) Find (i). lim f(x,y) (x,y)--(0,0) (ii). Is f(x,y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
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...
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...
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...
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv....
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv. Along y x2: ii. Along the y-axis: g(x, y) exist? If yes, find the limit. If no, explain why not. b. Does lim (r,y)(0,0) c. Is g continuous at (0,0)? Why or why not? d. The graphs below show the surface and contour plots of g (graphed using WolframAlpha). Explain how the graphs explain your answers...
(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
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
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
Q1. Let z = f(x,y) -√4x² – 2y² Find (i). domain of f(x,y) (ii). range of f(x,y) (iii). f(1,1) (iv). The level curves of f(x,y) for k = 0,1,2 4x2y Q3. Let f(x,y) = x2+y2 if (x,y) = (0,0) 1 if (x,y) = (0,0) Find (i) lim limf(x,y) (x,y)-(0,0) (ii). Is f(x, y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
Given the function f(r.y) lim f(x, y) (ry)-+(0,0) a. Evaluate iii. Along the line y= r: i. Along the r-axis: iv. Along y12 ii. Along the gy-axis: ,f(x, y) exist? If yes, find the limit. If no, explain why not. lim (a.)-(0,0) b. Does (0,0)? Why or why not? c. Is f continuous at d. The graphs below show the surface and contour plots of f (graphed using WolframAlpha). Explain how the graphs explain your answers to parts (a)-(c) above....
Q2. x+y (a). Let f(x,y) = x²+y²+1 Find (i). lim (x,y)-(1,1) f(x,y) (ii). lim f(x,y) (x,y)-(-1,1) (iii). lim f(x,y) (x,y)-(1,-1) (iv). lim f(x,y) (x,y)-(0,0) ( 4x²y if (x, y) = (0,0) Q3. Let f(x,y) = x2 + y2 1 if (x,y) = (0,0) Find (i). lim f(x,y) (x,y)--(0,0) (ii). Is f(x,y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
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...
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...
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...
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv. Along y x2: ii. Along the y-axis: g(x, y) exist? If yes, find the limit. If no, explain why not. b. Does lim (r,y)(0,0) c. Is g continuous at (0,0)? Why or why not? d. The graphs below show the surface and contour plots of g (graphed using WolframAlpha). Explain how the graphs explain your answers...
(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
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