1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y =...
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. 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 3x3 | 3y2 lim (2,3)(0,0) sin(2:3 + y2)
Find the limit lim (x,y) → (0,0) x2 + y2 a. Does not exits O b.o c. None of these d.
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.
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
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)....
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. Along y12 ii. Along the gy-axis: ,f(x, y) exist? If yes, find the limit. If no, explain why not. lim (a.)-(0,0) b. Does (0,0)? Why or why not? c. Is f continuous at d. The graphs below show the surface and contour plots of f (graphed using WolframAlpha). Explain how the graphs explain your answers to parts (a)-(c) above....
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)