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Problem 2: (2 marks) By considering different paths of approach, show that the following functions have...
3. Limits. The limits below do not exist. For each limit find two approach paths giving different limits Calculate the limits along each path. You may want to use Taylor series expansions to simplify the limits. sin (x) (1-cos (y) a) lim (y)(0,0 x+ PATH 1: LIMIT 1 PATH 2: LIMIT 2 b) lim (y)(8,0) cosx + In(1+ PATH 1: LIMIT 1 PATH 2: LIMIT 2
3. Limits. The limits below do not exist. For each limit find two approach...
5. (7 marks) Evaluate the limit, if it exists, or show that the limit does not exist. 51 + y 2.cy (a) lim (1,3)+(0,0) 5x + y + 9-3 (b), lim (x,y)+(0,0) x2 + y2
please answer both of them and show all the steps
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2 + y2
, (b) Find or show the limit does not exist:linm (x, y) → (0,0) x2 + y2 8, (b) Show that the following limit does not exist 2 lim (x, y) → (0,0) x2...
1. Find lim(x,y)=(1,1) x2-y2 2xy 2. Show that lim(x,y)-(0,0) 21 z does not exist 3. Show that lim(x,y)=(0,0) z?”, does not exist 4. Find lim(x,y)=(0,0) eye if it exists, or show that the limit does not exist
2.c)
2. Show that each of the following limits does not exist : (a) lim 1 + 2y (b) lim (2 + y) (x,y)--(0,0) -y (2.) +0,0) r? + y2 (d) 6ry lim (x,y)+(0,0) 24 + y (c) lim (x,y)0,0) - 2 + y
2. [1 mark] Calculate the limit of the vector valued function f: ACRY-R lim G logy) 3. Consider the function :R? - R. given by Flv = 0 if if (,y) (0,0): (x,y) -(0,0) (a) (1 mark] State the definition of continuity of a function at the point. (1 mark] Then calculating the limit (by any technique of your choice) show that f is continuous at (0,0). (b) [2 marks] Find the partial derivatives and at (x,y) + (0,0). and...
(4) Evaluate each of the following limits or show that the limit does not exist: (a lim 2014 – 2y4 (3,4) (0,0) 22 - y2 lim 1 + 2y (x,y) (0,0) = -2y (b)
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
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 (...
help me. ASAP
2. Show that the following limits do not exist 1.2. Limits and Continuity (a) lim(x,y)=(0,0) DEO (b) lim(x,y)=(0,0) 2,2*-*y2 (c) lim (2,3)+(0,0) 4x2-2y2 n(x,y)+(0,0) x2 - 3y2