Find f, fy, and f,, and evaluate each at the given point. z' fix, y, 2) %3D х*уз + 2хyz - 8yz, (-3, 1, 3) = X f(x, y, z) = f,(x, y, z) = f_(x, y, z) = f,(-3, 1, 3) = f,(-3, 1, 3) = f(-3, 1, 3) =

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, -5) and the direction in…

A: We have to find the maximum rate of change

Q: exist. :) Compute the linearization of f(x, y) at the point (x, y) = (1,1). %3D

A:

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

A:

Q: of of Find and for the furction f(xy,z) = x y+ y + xỉ ôx 'ay

A: For the function f( x, y, z ) = x2y + y2 + xz2 . We need to find some partial derivatives.

Q: 2. The function f(x,y,z) = xyz has gradient Vf(x,y, z) = (yz, cz, ry). Let C be the path from (1, 1,…

A:

Q: 5. Compute F-dà where F= zk and Sis the rectangular plate with corners (0, 0, 0), (1, 0, 0), (0, 1,…

A: To find -   Concept used -

Q: The maximum rate of change of the function f(x, y, z) = xyz at the point (1, 2, 3) occurs in the…

A: In this question we have to find the correct answer.

Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: (x, y) frx (x, y) fyy (x,y) f, (x,y) Point 1 1 Point 2 Point 3 -1 -1 -1 -1 1 Point 4 -1 -1 Point 5…

A:

Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

A:

Q: Use the Chain Rule to evaluate the partial derivativeat the point specified. ∂f/∂u and ∂f/∂v at…

A: The partial derivative of any function can be calculated by partially differentiating it with…

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

A:

Q: Correction: Bonus Assignment, Exercise 8: Exercise: 8 Evaluate 1-x²-y² e-3(x²+y²+z²)² dz dydx

A: Given,   from limit we can say this follow x2+y2+z2=1 put this value in integral…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

A:

Q: Calculate moment generating function of J = Y + Y2 + Y3 to determine distribution of J and its %3D…

A: Given that Y1, Y2, and Y3 are independent geometric random variables with parameter p.

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: Prove that div curl v = 0 where the components of v have continuous second partial derivatives

A:

Q: Find the local linear approximations L to the specified function f (x, y)= xsiny at the point P…

A:

Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

A:

Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

A:

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

Q: Let J be a function of two variables such that its first and second partial derivatives are…

A:

Q: Determine the type of points on the x(u, v) = (u, v, u²) surface. Differential geometry

A: Given point is Xu,v=u,v,u2.  This point is of the form Xu,v=fu,v,gu Let Xu,v=xi+yj+zk. Then,  x=u…

Q: what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)  (show all steps…

A:

Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= ○ (0, 2) O None of…

A: We have to choose correct option for all critical points.

Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

A:

Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Find normal line and parallel plane to the function f(x, y, z)=√xyz - 4 At point (1,2,8).

A:

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: u:(x, t) = и (т, Urz(T, t) u,(0, t) = uz(1, t) = 0 u(x,0) = f(x)

A:

Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= O None of the others…

A:

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: 2. Let closed curve C consist of the line segment from (0, 0) to (2, 1), followed by the line…

A: We will solve both parts of this question using basic knowledge of line integrals and definite…

Q: Find the symmetric equations for the normal line Ly to the surface S: f(x,y)=5√√² + y² at the point…

A:

Q: speed of a particle with position function r(t)=⟨8cost,−6t,8sint⟩r(t)=⟨8cos⁡t,−6t,8sin⁡t⟩ ⟨v(t)=⟨ ,…

A:

Q: Consider the function f(x, y) = y? + x² – 3z + 8 on the closed triangular region with vertices (0,…

A: Given function fx,y=y2+x2-3x+8

Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

A:

Q: Find the gradient of f(x, y, z) = xy tan (3z) at the point (x, y, z) - 3, 2 Find exact values. No…

A: Given,