Answer :
QUESTION 2 Find lim xy +1 (x, y)*(0,0) x2 +y2-1 O-1 O 2 00 O Does...
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
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...
Find the limit lim (x,y) → (0,0) x2 + y2 a. Does not exits O b.o c. None of these d.
Prove that the limit does not exist: lim (x,y,z)--> (0,0,0) (xy +yz) / (x2+y2+z2)
15. lim xy cos y (x, y)+(0,0) x2 + y4
(1 point) Consider the function defined by ?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2 except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0. Then we have ∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)= ∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)= Note that the answers are different. The existence and continuity of all second partials in a region around a point guarantees the equality of the two mixed second derivatives at the point. In the above case, continuity fails at (0,0)(0,0). (1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
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
Determine if the following limit exists. 4xy? lim x=>(0,0) x2 + y2
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...
Can you help with 4 and 6. 4. lim (x,y)-(0,0) x + x² + y + yx x + y 5. x² + y10 lim (x,y)=(0,0) x2 + xy + y 10 6. sin(x) + (y + 2)2 lim (x,y)--(0,0) X + 1