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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 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...
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
evaluate each limit or explain why it does not exist (b) 4x² - y² lim (x,y)+(0,0)...
evaluate each limit or explain why it does not exist
(b) 4x² - y² lim (x,y)+(0,0) x2 + 2y2
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...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it d...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
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.
(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
G 726y Evaluate the limit, if it exists: lim (x,y)+(0,0) 28 + y4 7 7/2 0...
G
726y Evaluate the limit, if it exists: lim (x,y)+(0,0) 28 + y4 7 7/2 0 Limit does not exist.
1. Sketch a few of the level curves of the function f(x, y) = surface z...
1. Sketch a few of the level curves of the function f(x, y) = surface z = y2 and then use these to graph the f (x, y) 2. Evaluate the following limits if they exist. If they don't, explain why not. (a lim (x,y)(0,0) + 4y2 x4-y4 (b lim (x,y)(0,0) x2 + y2 cos 2 y2) - 1 lim (c (z,y)(0,0 2ry (x, y)(0,0) Is the function f(x, y) continuous at (0,0)? 3 = (х, у) — (0,0) 2x2y...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a....
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
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...
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
evaluate each limit or explain why it does not exist
(b) 4x² - y² lim (x,y)+(0,0) x2 + 2y2
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...
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l
f(x, y) = y/(sqrt(z? + y2) + x)
Evaluate the limits below, if they exist. If...
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.
(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
G
726y Evaluate the limit, if it exists: lim (x,y)+(0,0) 28 + y4 7 7/2 0 Limit does not exist.
1. Sketch a few of the level curves of the function f(x, y) = surface z = y2 and then use these to graph the f (x, y) 2. Evaluate the following limits if they exist. If they don't, explain why not. (a lim (x,y)(0,0) + 4y2 x4-y4 (b lim (x,y)(0,0) x2 + y2 cos 2 y2) - 1 lim (c (z,y)(0,0 2ry (x, y)(0,0) Is the function f(x, y) continuous at (0,0)? 3 = (х, у) — (0,0) 2x2y...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
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