Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r cos y, –3 В. (2г, 2у, — 2:) C. (2r + 3, 2y – 4, cos y cos r – - sin a sin y – 22) D. 2r + 2y — 2г E. 0

Q: Continuity for Three VariablesAt what points (x, y, z) in space are the functions in Exercises 35–40…

A:

Q: f (sin(x²y), x³ – y²) ry If we take u = sin(x'y) and w x³ - y?, then: dz A) dy x2 . fu · cos(r?y) –…

A:

Q: Find y' at the point (7, 7) where z sin(z? – y*) + 46 = z² – 3. Türkçe: z sin(z² – y²) + 46 = z² – 3…

A: To find y' at (7, 7) Where  x*sin(x2 - y2) + 46 = x2 - 3....(1)

Q: In Exercises 61-68, compute the derivative indicated.

A: We have solved first three parts for you, if you want solution of other questions, repost them.…

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: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: Let f(2) = z e 2 #0. z # What type of singularity does f(2) have at z 0? (Justify.) What is the…

A: The singularity of the function f (z) have at z = 0  .     Find the Taylor series expansion of z5…

Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Transform the equation sin asinydx + cos acosydy = 0 to a variable separable form f (x) da + g(y) dy…

A: We will find out the required value.

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: Consider the functions z=7 ex In y, x= In (u cos v), and y= u sin v. dz dz (a) Express and as…

A: Given, z= 7 ex ln y    ....... (1)x= ln ( u cosv) .......... (2)y= u sinv…

Q: Q2) A) Verify that Wxy Wyx for w = x sin y+ y sin x+ xy. B) Show that f(x, y) = e-2y cos 2x…

A:

Q: Which of the following is not a homogeneous function? h(x,y)= xª − 3xy³ + y¹ − x² cos Option 1 b(x,…

A: Let's solve.

Q: Transform the equation sin zsinydr + cos xcosydy = 0 to a variable separable form f (x) dx + g(y) dy…

A:

Q: Calculate ôz/ðu and dz/ðv given the following functions: 2x – Y z = f(x, y) = x(u, v) = e²u cos 3v,…

A:

Q: F. dr, where F(x, y, z) = y sin zi + z sin æj + x sin yk and r(t) = cos ti + sin tj + sin 5tk, 0 <t…

A:

Q: If f(x, y) = 17e* cos x + 6 cot y, then the total differential of ƒ at ( 0, ÷) i : O df = 17 dx + 12…

A: f(x,y)=17e-xcos x +6 cot y

Q: (B) Find the potential function V = V(r, y) such that %3D + yi+ + r)j = V¥ 1+ x2 + y? 1+ x? + y? and…

A: We have to find the potential function ψ=ψx,y such that x1+x2+y2+yi+y1+x2+y2+xj=∇ψ and also evaluate…

Q: There exists a solution, F(x,y)=Dc, to (2- 2aye) da – (2ye + 3 sin y) dy = 0 such that - OF 2ye 3…

A:

Q: af du (a) f(x, y) = sin-¹ (b) f(x, y): = x+y (c) f(x, y) = In ( t = 1 and u = 2 af and where Ət 2.…

A:

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Linearizations for Three VariablesFind the linearizations L(x, y, z) of the functions in Exercises…

A:

Q: L fx, y, z) ds. Evaluate f(x, y) = 9y – x S: r(u, v) = cos(u)i + sin(u)j + vk Osus", 0 svs1

A: We have to evaluate the integral.

Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Calculate and ди dv using the following functions: х+ 2у — 4z 2х — у + 3z x = x(u, v) = e2u cos 3v =…

A: Partial differentiation is the differentiation of a function with respect to only one variable by…

Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

Q: If f(x, y) = 19e CoS I +7 cot y, then the total differential of fat (0.) is: 4 O df= 19 dr + 14 dy…

A: Let the function is f(x, y)=19e-xcos x+7cot y Total differential is defined as df=fx(x, y) dx+fy(x,…

Q: 1. x = t, y = 1/(1 +²), z = t² 2. x = cos 4t, y = t, z = sin 4t 3. x = t? – 2, y = t³, z = tª + 1 4.…

A: If any point (x,y,z) on the curve of a function can be represented in terms of a parameter t , then…

Q: /1+x² + y² dS where S is the helicoid: r(u, v) = u cos(v)i+ u sin(v)j + vk, with 0 < u < 5,0 < v< 4n…

A: Let I = ∫∫S1+x2+y2dS and r(u,v)=u cos(v)i +u sin(v)j+vk We know that dS=ru×rv du dv Consider ru =…

Q: Find fæ, fy, and fz. f(z, y, z) = z In(a"y cos(5z) 4.3 = z In (x*y° cos(52)) fr = fy = f: =

A:

Q: Give the function z f(x, y)=4x²+ 3y, x(t)=sin tand y (t)= cos t. zp =2sin t.cos t 2.1 Show that dt…

A: The derivative of the function can be calculated by differentiating the function with respect to the…

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: (e) z = x? + 2y2 where x = sin(t), y = 3sin(t) and t = dz dz answer: dt 19sin(2t) , = 19 dtlt=! (f)…

A: (e) Given z=x2+2y2 where x=sin(t),y=3sin(t) and t=π4. (f) z=cos(x)sin(y) where x=πt,y=2πt+π2 and t=3…

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

A:

Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: 1. Detanmne the rusutt OF a. Gradi ent f(x.y,z) ex sin cy) In (7) b. Divergenie =7? C Curl F=y2 t…

A:

Q: Q2: Expand f(x,y) = [sin (x y*)]² about (, 1). %3D Q3: Given T(u) = sin (u), where u = Vx² + y²,…

A: Here I am giving answer of 1st question is you  want answer of second question repost  the question…

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: Find the differential of the function f (x, y, z) = sin x?y³z4. %3D O 2xy³z* cos a?y³ zªd« O 2xy®z*…

A: Given f(x,y,z)=sin(x2y3z4)=ddx(sin(x2y3z4))We know that sin(x)'=cos(x)=cos(y3z4x2)*ddx(x2y3z4)

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

A:

Q: Consider f(t) = (cos t, sin t, t²) and g(x,y,z) = (x² + y² + z², 3x + 4y –- 12z) and h = g(f(t)) =…

A:

Q: 17. Suppose F = V × A, where A = (y + Vz)i + e»²j + cos(xz)k. Determine the flux of F outward…

A:

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: If f(x, y) = 22e¯ª cos x + 4 cot y, then the (0, is total differential of f at - O df = 22 dæ + 8 dy…

A:

Q: Evaluate     CF · dr. F(x, y, z) = xi + yj + zk   C: r(t)= 9 cos(t)i + 9 sin(t)j + tk,    0 ≤ t ≤ 2?

A:

Q: Given that F(x, y, z)=sin x i+cos yj+ xzk. Evaluate , F.dr where C is given by r(t)={r',-f,t) :…

A:

Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.