B). For what values of r, reR is the function [(x+y+z) ƒ(x,y,z) = { x² + y² +z² 0, continuous on R. [Verify using Mathematica (x, y, z) = 0 (x, y, z)=0

Q: Let f be a function such that Vf(x, y) = (2x, 1) g(x, y) = x² + y². Find all the points on the curve…

A: Let f be a function such that ∇f(x, y)=2x, 1 and let g(x, y)=x2+y2 We have to find all the points on…

Q: Consider ∂/∂t f(tx, ty). Prove that if f is homogenous of degree n, then the attatched equation is…

A:

Q: The function Arg(z) is discontinuous at Select one: O a z =x+iy :x = 0, y 2 0}. O b. (z = x + iy : y…

A: Result: Arg z is discontinuous at non positive x-axis. Let z=x+iy be a complex number. Suppose z is…

Q: Sketch a contour map for f(z. y) using the k-values, k = 1, 2, 3. |f(x, y) = |x| + sin(y)

A: Given : f(x,y)=|x|+sin(y)   To sketch : contour using the k-values k=1,2,3

Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: 2A) If this function were to be rotated around the horizontal axis in three dimensions, the…

A:

Q: The domain of f(x, y) is the xy-plane, and values of f are given in the table below. y\x 0 1 2 3 4 0…

A: Given that the domain of the function f(x,y) is the xy-plane and the values of f(x,y) are given in…

Q: .Consider the function f(7,4) = { xy x²+4y? if (x, y) # (0,0) if (x, y) = (0,0) O Is f continuous at…

A: Since the given function is of type function of several variable therefore

Q: Consider the function f (x, y) = cos(x sin(y)). The domain of f consists of all real numbers (x, y)…

A: 1. Domain of f(x,y)=cos(xsin(y))The function involves the cosine of xsin(y). Since both sine and…

Q: = y6 – x³ has any absolute Determine whether the function f(x,y) extrema on R² (i.e. it is defined…

A:

Q: f(xo+h, yo+h) = f(xo, yo) + [fx (xo, yo)h + fy(xo, yo)k] 1 + xo, Yo)h² +2fxy(xo, Yo)hk + fyy(xo,…

A:

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

A:

Q: Consider F and C below. F(x, y, z) = yzexZi + eײj + xyeײk, C: r(t) = (t² + 2)i + (t² − 1)j + (t² −…

A: In the given question we have to evaluate : a) The function f(x, y, z) .  b) Evaluate the integral.

Q: 5. Calculate the divergence of F = (7x², 9y, -52).

A: