1. Consider XPy4 lim (x,y)=(0,0) x2 + y2 Compute the limit along the two lines y...
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y = 0 and yma. 2. Let F(x,y) = sin(x”y), where = sin(u) + cos(u) and y = ew. Use the chain rule (substitution will earn zero credit) to find 3. Find the maximum rate of change of f(x,y) - eat (1,1) and the direction in which it occurs.
Find the limit lim (x,y) → (0,0) x2 + y2 a. Does not exits O b.o c. None of these d.
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...
Determine if the following limit exists.
4xy? lim x=>(0,0) x2 + y2
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
Calculate the next limit, if it doesn’t exist, then prove
it.
2 y (b) lim (x,y)→(0,0) sin' y + ln(1 + x2)
(1 point) Consider the function defined by F(x, y) = x2 + y2 except at (r, y) - (0, 0) where F(0,0)0 Then we have (0,0) = (0,0) = ax dy 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) Note: You can earn partial credit on this problem...
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...
15. lim xy cos y (x, y)+(0,0) x2 + y4
8.) (minimum along lines does not mean minimum) Define f: R2 and, if (a, y)0, R by f(0,0) (a) Prove that f is continuous at (0,0). Hint: show that 4r4y2 < (z4 + y2)2. (b) Let & be an arbitrary line through the origin. Prove that the restriction of f [0, π) and t E R. (c) Show that f does not have a local minimum at (0,0). Hint: consider f(1,12). to ( has a strict local minimum at (0,0)....