Let f(x, y, z) = 28 + sin°(cos æ) + ev° y+(z+æ²)5 cos y, and let F = Vf. what is V x F? %3D Select one: a. (f(x, 0,0), f(0, y, 0), f(0, 0, 2)) b. f(1,0, 0) + f(0, 1, 0) + f(0, 0, 1) O c. f(1,1, 1) d. 0 e. (f(0, y, 2), f(x, 0, 2), f(x, y, 0))

Q: Consider f(x,y) = cos(x² e³). Then which one of the following is correct O!. fx(x, y) = – 3 y² sin(3…

A:

Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

A:

Q: Find Vf at the given point. f(x, y, z) = 32³ – 2(x² + y²) z + tan '(4xz), (0, 2, 3) Vf\(0,2,3) f(x,…

A:

Q: F(x, y, 2) = 2y cos(2) I+ e sin(2) j + xe k, S is the hemisphere x + y? + 22 = 9, z 2 0, oriented…

A: Surface integration

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

A:

Q: If z = f(x, y), where x = r cos 0 and y = r sin 0, show that a²z 1 a°z 1 əz r дr дх? dy? дr?

A:

Q: If U(x, y) =-e Y sin x and f(z) = U(x, y) + iV(x, y) is analytic, then V(x, y) = %3D -e cos x e cosx…

A:

Q: find 19. || xy cos y dA, R: -1 < x < 1, 0< y<T 20. y sin (x + y) dA, R: -T < x < 0, 0 < y < 21. et-y…

A:

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x*yt cos(2)) 4,4 fm = fu f2 =

A:

Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find f,(1,2,0). Leave your answer correct to two decimal…

A: We can find the answer as below.

Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

A:

Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

A:

Q: V, = {2i} m/s V, = {0.448v½i + 0.894v,j} m/s = {5 cos 0 i + 5 sin 0 j} m/s %3D 目。 Vb/r v, = 2 m/s 5…

A:

Q: Graph the following vector fields

A: (a)known fact:

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f,(8,2,0). Leave your answer correct to two decimal…

A: Partial differentiation of f(x,y,z) with respect to x is calculated by treating y and z as…

Q: Evaluate: y +y = - cos X COSX A. y = 0, sinx + Ca cosx + x sin x 8. C, COSX + Ca casx t x cas X C. y…

A:

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

A:

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: I need the answer as soon as possible

A: As we know that, eiz=cosz+isinz                   ...(1)And,e-iz=cosz-isinz                ....(2)…

Q: (a) f"(x) = e* – 2sin(x), f(0) = 3, f(1/2) = 0 (b) f"(t) = Vt – cos(t), f(0) = 2, f(1) = 2 -

A: The formula used: (i)∫ex dx=ex+c(ii)∫xn dx=xn+1n+1+c(iii)∫sin x dx=-cos x+c(iv)∫cos x dx=sin x+c

Q: Let z = e* + In( y), x = sin (uv), y° = cos (uv). 2 Determine at u = 1, v= 3

A: Topic- partial derivatives

Q: f f(2) = / cos(t) dt, then f'(x) = %3D COS Select one: a. 3e cos(a?) b. e cos(ez) c. 3e cos(e6z) d.e…

A: Given : fx = ∫1e3xcost2dt

Q: The function z = r' y is defined on the astroid r = cos 0, y = sin 0 where 0 < 0 < 2ñ. Use the dz…

A:

Q: Find * if y = y(x) on D is the domain of y(x). (II) (B + 2)y(«+1)cos[(a + 2)x] = x(«+1) + sin [(ß +…

A: Take the derivative of each term and than simplify.

Q: d(x,y) x(u, v) = sin(u) + cos(v) and if a(u, v) y(u, v) = – cos(u) + sin(v). 1.

A: Given xu,v=sinu+cosv and yu,v=−cosu+sinv We have to find the Jacobian ∂x,y∂u,v. The Jacobian…

Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: F(t, x, y, 2) = [0, cos(t), sin(t)] x 7, 0<t<

A: Solution

Q: Find D (x, y, z) where f(x, y, z) = cos(z²)sin(y²) In the direction of v = (4, 15, 18). %3D Possible…

A: Introduction: The formula for the directional derivative of the function f(x,y,z) in the direction…

Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

A:

Q: U + ru, =x u(z,0) = sin(87x) cos(90r). IE R, t> 0,

A: Given ut+xux=x2 By Lagrange's method , we get dt1=dxx=dux2 By equation (1) and equation (2) , we get…

Q: Find fa, fus and fz. f (x, y, z) = (5z)) 3z In (x*y cos

A:

Q: a. Show that If z=x+iy where y >0 Then: 0 < |e*|<1 b. Evaluate cos (i z) – sinh?(z)

A: Using De Moivre's Theorem

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

A:

Q: Utt || for 0 < x < T u(x, 0) = x? u:(x, 0) = }cos(8x) Uz(0, t) = u„(r, t) = 0

A:

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find fy(5,5,0). Leave your answer correct to two decimal %3D…

A: Partial derivatives

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

A:

Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

A:

Q: R. 4, = U, - sin x cos t, :>r > 0 B.C.: «(0, t) = 0, 1.C.: u(x, 0} = 0, 1,(x. 0) = 0

A:

Q: f z = f (x, y), where x = r cos 0 and y = r sin 0, show that a2 z 1 a²z 1 dz ar2 ar2 p2 aA2 r ar

A:

Q: . и., — и. — sin x сos t, t>0 В.С.: и(0, г) %3D0, 1.С.: и(х, 0) %3D 0, 1,(x. 0) = 0

A: Solution :-

Q: Integrate f,-¿ S=; cos x²dx dy =1 (x= 1 y=0 Jx=y Select one: a. cos1 b. .5cos1 C. sin1 d. Non of…

A: We will find out the required value of given integral.

Q: Calculate the Cauchy principal value. 8 COS X V.P. Leta -dx, (a > 0). (a²-x²)

A: We solve by using residues.

Q: Let u(x, y. z, t) = [sin(ax) + cos(bx) + sin(cæ)]e-(k+1)*t. Find a, b ,c if u = Ugr + Uyy +Uzz•

A: NOTE: Please ignore the sheet.

Q: Given f(x, y) = 7æ° cos (y*), find .9 COS fzy(x, y) = fyy (x, y) = %3D

A: Given  f(x, y) = 7x9 cos(y8) To find fxy, fyy

Q: aw (a) Calculate ди aw and dv using the following functions: x + 2y – 4z = f(x,y,z) = 2х — у + 32 x…

A: Partial derivative of multivariable function with respect to any of the variable is obtained by…

Q: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

A:

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

A: