4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x = 0.

Q: dw If w = x'y sinz - 3zexy, find dz O a. dw =x?y cosz - exy dz %3D O b. dw =2x2y cosz -exy dz Oc. dw…

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Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

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: Given z = 9t – 11 and y = 81 sin t %3D dy (i) dz dy (ii) dx?

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given data:     The expression for the given electrical potential function is: V(x,y,z)=3x2-2xy+xyz.…

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: dz Find when u= 0, v= 1 if z= sin(xy) + ysin(x), x = uv, y3Du² +v?. du

A: Given  z = sin(xy) +ysin(x)              x = uv and y = u2 + v2  Substituting x and y in z we have…

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: if t(uバ) = ta y u= X Cosy V = X siny ニ Determine JR to つメ

A: Given      If    f(u,v) = tan-1(u/v)    u = x cosy    v = x siny

Q: Match the D.E. with a direction field: y' = t+ y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2…

A: NOTE: The horizontal axis is t-axis.

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: dt z = cos(x + 4y), x = 5 t ³, y = 8/t

A: We need to find out the value of dzdt

Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: Find the solution of the IVP. y" + 3y' + 2y = 20 (sin t + 8 (t – 1)), y (0) = 1, y' (0) = –1

A: We solve the given initial value problem by using Laplace transform.

Q: Find a. Əw dx a. aw əx and b. y (2π,1,-π) Əw at the point (x,y,z) = (2π, 1₁ - π) if w = x² + y² + z²…

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

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

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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…

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

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Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: Q5.a) Find if sec?y = x? + t² dt Jsiny dx dy b) Find if tan?y = x² + Jysinx cotx VE2 +1 dt tZ+Idt

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Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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

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Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

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Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

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Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: siven f(x,y,z) = sin (3xy) + 3xyz3. Find fxzy(3,2,2).

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Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: Ex: verifay u = e* cos y is a solution of laplace eqution

A: Solution:Given             u=ex cos yTo verify u is a solution of Laplace equation:i.e.,…

Q: Al/ compute 6(4+ ec©*) dx + (siny + 3x?)dy cosx Where c is closed bounded region lying in the first…

A: Given (A) The given integral is ∮4+ecosxdx+siny+3x2dy and the region lies in between x2+y2=4 and…

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

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Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: Find (∂ w/∂ x)y, z if w = x2 + y - z + sin t and x + y = t.

A: To find the partial derivatives.

Q: If z=x+ iy=r(cos(0) + isin(@))then |z|=Vx²+y² =rO Z=r0 arc z=00

A: Given z=r(cos θ +i sin θ)   Modulus of complex number, |z|=x2+y2