Explain how the evaluation for each of S. f(x, y) ds, ſ. f(x, y) dx, ſ. f(x,y) dy, and F ( x, y) · d T involves a process similar to trig substitution. Assume that х, C is defined by r(t) = over the interval [a, b].

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: Find div F for F(x. y, 2) = (xy, 5 - zy, x +y). Select the correct answer below: O x- O y-? O x-5- O…

A:

Q: Let F(u, v) be a function of two variables. Find a formula for f′(x) when             (a) f(x) =…

A: Given fx=F4x-4hence u=4x , v=4f'x=∂F∂u.∂u∂x+∂F∂v.∂v∂xBy chain rule      =∂F∂u.∂∂x4x+∂F∂u.∂∂x4…

Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

Q: The function g(x, y) has tangent lines at the point (1, 2) with directions and . Find Vg (1,2).…

A: Given that:  Tangents at point (1, 2) are:  <2, 0, 8> and <0, -1/3, 2>

Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

A:

Q: Consider the function f : R2 → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following…

A:

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

A:

Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

A: We have to fund the value of gv(u=-1,v=1).

Q: Compute fFdr, where F(x, y) = (5+27x², 2xy) and C is a line segment from (0, 0) to (1,2). (Use…

A:

Q: Let (x, y) E R × R. Consider the following functions from R? to R? a((x, y)) = (-x, y) and b((x, y))…

A: Order of the function

Q: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

A:

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

A:

Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

A:

Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

A:

Q: Q2: Find ôf ôf - for the function f(x, y, z) = x²y+ y° + xz² and Əx 'dy

A: We will find out the required values.

Q: The Range of y = [2x + 1] is Z, TO F

A: As given function is Greatest Integer Function and we Know that greatest integer function is…

Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

A:

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

A:

Q: Find real numbers a,b,c,d such that And then find f'(z) =? f(x) = x² + axy + by² +1(cz² + day + y²).

A:

Q: h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where…

A: Suppose X and Y are jointly distributed with pdf  where .