Let x = (-2,7,-7) and y = (1,6, 6) be in R°. Compute the following: x + y = ( -5x x – y = ( -5 x + 8y= (

Q: If an object is moving with v(t) = 3¹ and the position X(1) = 2, what is the position of the object…

A:

Q: Find f, and fy, and evaluate each at the given point. f(x, y) = arctan(), (2, -2) f,(x, y) = f,(x,…

A:

Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: Q3. If u = e'' sin'p, p=sinx, q=z²Iny, r=1/z, use chain rule to find ди ди > ах ду , and ди

A:

Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

Q: Find the real component if mid 09.png s(e)= a in vbet is evaluated at z = 9 + 4i when a=8 , b = 7,…

A:

Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Hw÷ find the Voctor Peralle I to the line intersedbetween the two flane 3X-6y-2Z=5 and 2x+4-27=5

A: The equation of the given planes is, 3x-6y-2z=52x+y-2z=5 If n1 and n2 are the normal to the planes,…

Q: where C is rE by the lines X

A:

Q: Find f. (12z + z?) dz, where C is the boundary of the rectangle with vertices at the points 1+2i, –…

A: As you have asked more than one different question, we shall solve first question only. For others,…

Q: If u(x,y) =3x2y+2x2-y3-2y2, then u is harmonic %3D

A: A function u(x, y) is said to be harmonic if it satisfies the differential equation uxx+uyy=0. The…

Q: For the function f(x,y,z) = In (5x + 4y + 9z), find f,, fy, and f,.

A:

Q: Let ƒ(x, y) = x2 - xy + y2 - y. Find the directions u and thevalues of Du ƒ(1, -1) for which Duƒ(1,…

A:

Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

A: To find the derivative of the given parametric vector, we need to differentiate each component of…

Q: z= em and a = 2t– 2s?, y = 2s – 2t, find az at t = 1, s = 1. at

A:

Q: b) Find the work done along AB A(1,-1, 2) F=5i + 3j + 2k B(3, 2, -4)

A:

Q: Find fx and fy, and evaluate each at the given point f(x, y) = sin xy, (2,  /4)

A: the given function is f(x,y)=sinxy. the given point is (2,1/4)

Q: For each non-homogeneous ODE, find the basis for the corresponding homoge- neous equation. Then,…

A:

Q: Hw.L showthat Vi=3inbj andVz 2-i-zj have opfosite directions.

A:

Q: Find r(t) and v(t) if a(t) = 8 cos(t)k, v(0) = 4i + 6j, and r(0) = 7i. v(t) r(t) %3D

A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

Q: Find the imaginary component of In(z + w) if z = 16 + 6i and w=7+8i . Round off your final answer in…

A: Complex number, imaginary part

Q: Find f, and f, and evaluate each at the given point. fx, у) - arctan(), (2, -2) fx(x, y) = ,(x, y) =…

A:

Q: * Find grad A at p (1, -1, 1) for A = 3x² y z %3D - 6 i+ 3j-3k O 6 i +3j+ 3k O - 6i O -3 O Simplify…

A:

Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D d) – 2 e) - 4 g) None of…

A:

Q: Let y: (0, 3] → R?, y(t) = (t,?V³) and I := ran y. Sketch T and compute L(T) :!!

A:

Q: U is y= cosx. A

A:

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

A:

Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

A:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

A:

Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

A:

Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

A:

Q: For D E BC of AABC ВА BD AD bisects ZBAC. АС DC Select one: True False

A:

Q: Given f (x, y) = x cos y - ye*, find fx and fy. Compute Dif (3,-2) and Daf (3,-2) if f(x,y) = 5x3 –…

A:

Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

A:

Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: 16. QT is a midsegment. Find x and y. PT = x- 10x, TS = 24, QR = 6-y, PQ = 2y+ 3 R

A:

Q: Find T, N, B, K and t for r(t) = (3csc^3t • sin^6t) i + (3sec^3 t • cos^6t)j + 5k

A: given that                                             r→(t)=3csc3tsin6ti^+3sec3tcos6tj^+5k^ now…

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and…

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

A:

Q: use the methor of undetermined coefficients to find the gen. sol to: y'' - 3y' +2y = t2 + 2 e-t

A:

Q: Identify the domain, ra nge and equation of the asymtte's for Hnis equation: y X+2 X²-4

A: Given equation: y=x+2x2-4

Q: If f(x,y,z) = In(xz) - 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D -3 d) – 2 e) - 4 g) None…

A: ANSWER

Q: Find f, and f and evaluate each at the given point. 2xy KX, y) = + 2y (1, 1) ,(X, y) = F,(1, 1) =…

A:

Q: Find fx and fy, and evaluate each at the given point f(x, y) = cos(2x − y),           ( /4,   /3)

A: Given,  cos(2x − y),