Verify that fy = fx, for the function f(x,y) = x° + 3y° +7. 9 For the function f(x,y)=x° + 3y° +7, fxy = fyx and f, =. Therefore, fy = and fx since %3D %3D %3D

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Which of the following functions is homogeneous of degree 2/3. option I: 3 f(x, y) = /x² + y2 option…

A:

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

A:

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: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Utt = Uxx, x>0, t > 0, u(x,0) = f(x), u₁(x,0) = 0, u₂(0,t) = 0, where f(x) = { b) Sketch the…

A: solutions are given below:

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

A:

Q: Find the linear approximation to the equation xy f(x, y) 2. at the point (4,6,4), and use it to…

A:

Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

A:

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

A:

Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

A:

Q: Compute the directional deri vative of the function f(z,y, 2) = zy² + y²9+°% at the point P(4, –2,…

A: Given function is fx,y,z=xy2+y2z3+z3x

Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

A:

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

A:

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A:

Q: Find the linearization of the function f (z) =23 at z = 1. L(z) = Using this linearlization, f…

A:

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

A:

Q: Find f, and fy. f(x, y) = 5x In xy %3D %3D fy =

A: Solution: The objective is to find the partial derivatives

Q: Find the linear approximation to the equation f(x, y) = 3, xy at the point (8, 4, 6), and use it to…

A: To find the linear approximation to the equation at point (8,4) Given that f(x,y)=3√(xy)/8

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

A:

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

Q: Find ( fx, fy, fz» fxy » f yx » f xyzf zzx) for the function: ух f(x, y, z) = xyz +x²y + z³x+ x²y²

A: Given:

Q: Show that the Cobb-Douglas function F(x, y) = bx" y" satisfies the equation ƏF ƏF + y (n + m)F(x, y)…

A: Given that the Cobb-Douglas function F(x,y)=bxnym We have to satisfies the equation…

Q: For the function f(x, y, 2) = 102° y³z+ 7æy®z4 + 19xz2 + 8y%z4 + 5a° + 17y7a11 + 4xyz +23 compute…

A:

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

A:

Q: Verify that fy fyx, for the function f(x,y) = 3x° +4y+ +7. %3D For the function f(x,y) = 3x° +4y° +…

A:

Q: (2) In Exercises 1-3, find fx, fy, and fz. 1 f(x, y, z) = 1 + xy² – 2z? |

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

A:

Q: Find the lineanzation LlXiy) of f (iy) =x*-5Xy at (2,1). Then use the linearization to approximate f…

A: Here in this question we need to linearize the given function and then approximate the value of…

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: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

A:

Q: Evaluate F.dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise around the…

A: The objective is to evaluate ∫CF·dr where Fx,y=2y-3cosxi+4x+6sinyj and C goes counterclockwise…

Q: Suppose that f(0) = 1, f(0.5) = 2.5,f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidat rule with…

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: 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 :

Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: X+Z+3Siny X +2y-2

A:

Q: Consider the function f(x,y) = (3x^2 + bx)(2y^2+dy) where b and d are non-zero constants. Determine…

A:

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A: