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.
15. lim xy cos y (x, y)+(0,0) x2 + y4
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)
- 3e - sin(-5x) Find lim - 2x (x,y)+(0,0) -3e - sin(-5x) lim - 2x (x,y)-(0,0) (Type an integer or a simplified fraction.)
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
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
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
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...
QUESTION 2 Find lim xy +1 (x, y)*(0,0) x2 +y2-1 O-1 O 2 00 O 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...