DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI | Let the following function be: G(x, y, z) = (5 cos(x) yz ²)i + (3e* si n(y) z³)j — (xyz−¹)k Determine at the points (1,1,1): a) Divergence of the function b) Rotational function

Q: QUICK CHECK 3 Let u(t) = (t,t, t) and v(t) = (1, 1, 1). Compute d (n(t) • v(t)) using Derivative dt…

A: given vector  Here use product rule : ---------------(1) Now we need to find derivative of u'(t)…

Q: Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.

A: Use the Gauss’ Divergence theorem,: Use the Gauss’ Divergence theorem,

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

A:

Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ (a) Find…

A: Given fx,y,z=yz+nx2y+yz3 Substitute n=5 Hence, fx,y,z=yz+5x2y+yz3 (a) We have to find the equation…

Q: Find the f(z) = u(x, y) + j v(x, y) for which X b) u = e cosy most general analytic function

A:

Q: Let r be the function defined by r(t) = (/10sen t,t, /10 cos t) where the coordinates of r(t) are…

A:

Q: Let z = f(x, y) = x² + y² be the temperature at a point (x, y) = R². (a) Draw a sketch indicating…

A: We know that the directional derivative of a function z=fx,y at a,b in a direction v→ is calculated…

Q: If the covariant tensor has components in Cartesian coordinates x',x². Find its components in polar…

A:

Q: ƒ (x, y) = k (x² + ²2/2), x ≤ (0,1), y = (0,2) Find k so f is legitimate joint pdf

A: Given that f(x,y) = kx2 + xy2    x∈(0, 1) y∈0,2 For legitimate joint pdf ∫02∫01f(x, y) dx dy =1 Now,…

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: (b) In(2x2 + у — 23) %3D х

A:

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: 3) To find the partial derivative of f (x. y) with respect to y at the point (xy. we A)…

A: Solving the question with an example

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

A:

Q: Consider the following vector-valued function: y : (−π,0) × (−1,1) → R³, y(u, v) = {cosh (v) cos(u),…

A: Consider the given function  defined as follows..We need to sketch the full image of .

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

A:

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: Use the theorem to find the slope of the line x = 4t, y = 2t, for - ∞ < t < ∞.

A: According to the theorem, the slope is given by - dydx = dydtdxdt…

Q: a) Describe the curve obtained when we make y = 2 and z = √2 . af b) Represent on this curve the…

A:

Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: Let C be the curve connecting (0,0,

A: Given that C be the curve connecting  (0, 0, 0) to (1, 4, 1) to (3, 6, 2) to (2, 2, 1) to (0, 0, 0).…

Q: a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf…

A:

Q: Exercise 5 3x + ax + b x² +1 Conşider the function f that is defined over IR as: f(x) = Where a and…

A: