Exercise 2: Find the limit if it exists, or show that the limit does not exist (10pts) lim (5x - xy?) ( 2.2) lim e "cos(x + y) 4 - xy lim (x,y)=(2, 1) x + 3y? lim In (1.0) 1 + y2 x + xy lim (29) 0,01 x + 2y? 5y' cos'x ( 20) x + y y sin? lim (y)-> (0,0) x + ху - у lim (y=0.0 (x - 1)2 + y2 xy lim lim (...
Find the limit, if it exists, or show that the limit does not exist. 1. lim (x²y3 – 4y?) (2,y)+(3,2) 2. lim 24 - 4y2 (x,y)+(0,0) x2 + 2y2 3. Find the first partial derivatives of the function of f(x,y) = x4 + 5.cy 4. Find all the second partial derivatives of f(x,y) = x+y + 2.x2y3 5. Find the indicated partial derivatives. f(1, y) = x^y2 – røy ; farzz, fryz
1. Consider XPy4 lim (x,y)=(0,0) x2 + y2 Compute the limit along the two lines y = 0 and y = mx. 2. Let F(x, y) = sin(x2y?), where x = sin(u) + cos(v) and y = eutu. Use the chain rule (substitution will earn zero credit) to find ƏF au
1. In each of the following: if there is a limit, calculate it; if there is no limit, explain why. Use any technique of your choice. (a) 2 marks] lim 2.xyz (2,y)-(0,0).<3+y3' (b) [2 marks] lima cos (x2 + y2) - 1 (x,y)--(0,0) x2 + y2
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....
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.
can you help me with two question, please 1/1 points v Previous Answers SESSCALC2 11.2.009.MI. My Notes Find the limit, if it exists. (If an answer does not exist, enter DNE.) Xy lim (x, y)-(0,0) x2 + y2 O , 1/1 points Previous Answers V SESSCALC2 11.2.015. My Notes Find the limit, if it exists. (If an answer does not exist, enter DNE.) Xy + 5yz? + 6xz (x, y, z)=0.0.0) x2 + y2 + 24 DNE ,
21. Is the following function continuous at (0,0)? Hint:lim 1-cos T (1-cos(x2 +y2) f(x, y)=11-cosztym if(x,y) (0,0) if (x,y) = (0,0)
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...
1. Find the maxima of the following functions. (a) f(x)-2-4. )2 (c) f (z,y)2+3. (d) f (x,y) = xy-x2-y2 + 9y.