g(x, y) = = sin(xy) xy Prove that g is continuous on R². if (x, y) = (0,0) if x = 0 or y = 0.

Q: what is f'of x

A: Find f’(x).

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Let f(x, y) = x/y. Then the directional derivative of f in the direction of √2 point (1, 1) is ○ (1,…

A:

Q: 6. Show that f(x) = sin x is uniformly continous on R.

A:

Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

A:

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

A:

Q: Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) = (0,0) (x, y) =…

A: g(x,y)=(xy/(2x2+y2), (x, y) not equal to (0,0)               0                 ,(x, y) = (0,0)

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: 2x'y+x?y? + 3xy³ 16x4 – y4 if (x, y) # (0,0) Let f(x, y) = if (x, y) = (0,0) Determine the set of…

A: