Evaluate \(\iiint_{\mathcal{B}} f(x, y, z) d V\) for the specified function \(f\) and \(\mathcal{B}\) :$$ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 16,0 \leq y \leq 5,0 \leq z \leq 2 $$\(\iiint_{\mathcal{B}} f(x, y, z) d V=\)
Evaluate f(x, y, z) dV for the function f and region W specified. f(x, y, z) = ex + y + 2; W: 0 SX S 4,0 S Y S x, 0 sz s 2 eBook
Discuss the Continuity of the function and evaluate the limit of f (x, y) (if it exists) as (x, y) + (0,0). f (x,y) = ln (x2 + y2)
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Given the constraint, find the stationary points for the following function and evaluate the second order conditions. Use the language technique. Subject to X2ザ=6 f(x,y)=ln x +2 lny Subject to X2ザ=6 f(x,y)=ln x +2 lny
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
8. w = yz2 - xLet x = e-t, y = ln (r + 2s + 3t) and z = yrs +t Evaluate 5. Find a function g(x) such the function f is continuous in R2 f(x,y) = { 0, x+y (g(x) ,x=y 6. f(x,y) ==*-1*32*** 1-xy please do 8 and 6 the same instructions as 5 please
Find fx, fy, and fz 5) f(x, y, z) = ln (xy)?
8. Evaluate the triple integral of the function f(x, y, z) = 6x over the solid region E that lies below the plane r+y - 2 = -1 and above the region in the ry plane bounded by the Vy, y = 1, and r=0. curves =
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)