2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

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

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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: Solve the follo wing in itial Value problem by using laplace trans formi- 9y =0 ; yl0) =0 and…

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Q: 4. Evaluate 2.x cos y dx – x sin y dy along the elliptical path + y? = 1 from (2,0) to (0, 1)…

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Q: (1) Evaluate the line integral 4xy dx + (2x² – 3xy)dy if the curve C consists of the line segment…

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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: So lve the di fferential equation dy + y - ecos x = 0,0 s x s0.5, y (0) = 0 by (a) Milne's me thod…

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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: 4. y = c, sin wt + c, cos wt w is a parameter

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Q: A) The position of a particle P(x,y) at time t is given by: x= (2t +3) , y =+t.Find the distance it…

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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: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

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: ula 0ニ こ0 2

A: Find solution using variable separation.

Q: Soru 6 dz Find when u= 1, v= 0 if z= sin(xy) + xsin(y), x = u² + v, y3 uv. av A 2 -1 D -2

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Q: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

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Q: (e* + In y +) dr + + In a + sin y) dy = 0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: Compute yarctar y? = 1 – 1+ y? ctan(y)dy. Hint: Note that 1+ y? fractan(g)dy- +C

A: we have to comloute the integral ∫ y tan-1 (y) dy we solve this integral by integration by parts…

Q: Ju こ0 二0 on 2) ne 「Xこo u la,e)=0

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: If y(u) = Cos v -dv then y'(u) =

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Q: 1 ezt dz 2ni Izl=2 z2+1 cos (t) o tan (t) o sec (t) o sin(t) o

A: See the attachment

Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

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Q: au %3D ax at u(x, 0) = 0 ди (x, 0) = 0 at u(0, t) = sin? t u(1, г) — 0,

A: Given,           ∂2u∂t2-∂2u∂x2=0                       for 0&lt;x&lt;1, t&gt;0      ...(1)u(x,…

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: |0 (x, y, z) | dV dz dr de |0 (z, r, 0)

A: In cylindrical coordinates

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: 4.x cot (y), where x = v ln(u) and y = 2uv. dz (a) Compute du dz (b) Compute

A: Given:                 z=x3ex-4x cot(y)wherex=vln(u)y=2uv Let's substitute the values for x and y:…

Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Find au explicit solution for the IVP. (Show work.) dy y? = 2ty", y(0) = dt 4

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Q: um,0) =)0 sn So

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Q: dw Let w =xycosz, where x = t°, y =ť, and z = arccost. Find dt

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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: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

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Q: 50. w = sin x + y²z + 2z, arcsin(t – 1), y = t³, z = 3 %3D

A: Since you have posted multiple question in this question which are not interlinked so I have solved…

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: What is the area of one of the petals of the rose curve r = 2 cos(20)? T/4 cos (20) d0 8. cos (20)…

A: We have to find

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: d the val 5) y= 2cos 30 6) y= 4sin 20 cos 0 7) cot F 7) y= sin (0-45) 8) y = 2 + cos 0 9) y= 3sin…

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

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

Q: The radius r and height h of a right circular cone are related to the cone’s volume V by the…

A: If r is the radius and h is the height of right circular cone, then find the following parts.a).…

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

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Q: Find Particular Sol. of  xsin2 ycosy y' + sin3y/ 1+lnx = 4 ; y(e)= π/2

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