1. Let f(z,y) = cos(z - y) and C be the line segment from (-1,1) to (3,-2). Set up but do NOT evaluate the following: f(x,y) ds

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y.…

A: To apply chain rule for this problem, we first need to identify the composite functions involved.…

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: IX. Į F dF where F = (x,y) and C is the straight line from (2,3) to (4,0)

A:

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

A:

Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

A:

Q: Evaluate Əw at (u,v) = (1,2) for the function w(x,y)=xy-y²; x = u-v, y = uv. ди OA. -1 B. 3 O C. 1…

A:

Q: Let f(x,y,z) = 2 In (xy+2). Find f(0,1,3), F(-1,-2,4 and F(2,1,-1).

A: We have a function f(x, y, z) = zln⁡(xy + z). We need to evaluate this function at three different…

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

A:

Q: D(3, 7) E(6, 1) F(20, 8) Is the line joining D to E perpendicular to the line joining E to F?

A:

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

A:

Q: Two sharpshooters will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's…

A: Given that, the errors are modelled by X1~N(0,0.5),X2~N(0,1). To solve this problem z table values…

Q: 3. If z = f(x, y) with the relation xy²z³ + x³y?z +1 = x + y+ z. Find dz at (1, 1, 1).

A:

Q: +3. . Find the linearization of _9). Can you tell anything about the error? at (3,2). Evaluate at…

A:

Q: H.W: Find f, fw, fx and fy if f(x, y) = x+ y+ xy yy>

A:

Q: Find fx and fy for f(x, y) = 2x³ + x³y² + 3xy² + y ³ Select one: a. fr = 4x² + 6x²y² + 3y², = 6x² +…

A: Given function:- fx,y=2x3+x3y2+3xy2+y3

Q: Calculate fw(-1, 2, 0, – 1) where f(x, y, z, w) = xy²z – xu? – e2²-y²–2²+2w=

A: Given that fx,y,z,w=xy2z−xw2−e2x2−y2−z2+2w2 To calculate: fw−1,2,0,−1

Q: 5. Let (ryz)" a) Compute the directional derivate of f(ay2) at the point (1.1,-1) in the direction…

A:

Q: Let f(x,y) = In (x³y). If fx(6,2)=fy(5,a) what is the value of a? а. 1 O b.-1 O C. 0 O d. 2 O e. -2

A:

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

A:

Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

A:

Q: 5. Let (ryz) 1+7 a) Compute the directional derivate of f(r.y) at the point (1.1,-1) in the…

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: A jungle has 400 monkeys, and it is estimated that the maximum population of the monkeys in the…

A:

Q: 6. The function f(x, y) = (x², y², xy) is a function of f : C² → C³. Determine whether the function…

A:

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

A: