2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer works.

Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

A:

Q: Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01,…

A:

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

A:

Q: Find fzyæ. f(r, y, 2) = a'y"2³ + xy® + y°z %3D f zyz

A: Given f(x,y,z)=x^4y^7z^5+xy^6+y^7z

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

A:

Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

Q: Find the linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the…

A: Given that  f(x,y,z)=√(x^2+y^2+z^2) To find the linear approximation of f(x,y,z) and also find the…

Q: Find fzyæ. f (x, y, z) = x°y®°z° + xy° + y°z f zyr ||

A:

Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

A:

Q: Find the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

A:

Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

A:

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

A:

Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

A:

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: Suppose that the only Införmation we have ab8ut a fuRcEiOH FIS y= f'(x) (a) Use a linear…

A: Given: f(1)=-7

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: Find fzya. f (r, y, 2) = x°y*z" 5.8 + xy* + y°z %3D f zyz

A: Given data÷

Q: Find the linear approximation to f(x, y) = 3, xy at the point (4, 6, 6), and use it to approximate…

A: brief explanation is given below.

Q: f(x, Y, z) =

A: We are asked to find the gradient of the function.

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

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Find f, and f,. f(x, y) = 13x In xy

A:

Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

A:

Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

A:

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

A:

Q: Let f(x) = x“.4x3 Find the derivatine of P (x) and the points, (X,y), where te tingent line is…

A: f(x) = x4 - 4x3f'(x)=ddx(x4 - 4x3)f'(x) =4x3 - 12x2

Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

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: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Find the linear approximation to f(x, y) f(6.11, 4.17) f(6.11, 4.17) = 5, xy at the point (6, 4,…

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: Let F(x, y, z) = x³yz² – 6x?yz + 9xz – 5y°z. Find F %3D xyz Fxyz

A:

Q: The gradient of f(x, y) is defined as Vf(2, y) = fa(x, y) + fy(x, y). %3D

A: We know that,             If f is afunction of two variables x and y , then the gradient of the…

Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

A:

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

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the image of the line z =3 +iy under f(z) = e

A:

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :