Evaluate Js I | ix, v, z) ds. Ах, у, 2) - Ху S: z = x2 + y2, 9 sx² + y2 < 81

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). =1 a(x,y)'a(u,v)

A: Given x=u1−v and y=uv We have to verify ∂u,v∂x,y⋅∂x,y∂u,v=1 Solve x=u1−v and y=uv for u and v, we…

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

A:

Q: (R) Let f(r,y) --In (1+ + y) and u= A- then Duf at (0,0) ia

A:

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: let KER bea parame tar and set feC) =63x- 2 イフx Othenuise %3D - 2x 43 Gue An expliect expressian fer…

A:

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

A:

Q: Find a, b, c in Q such that (1 + VA/(2 – V2) = a + bV7 + cVA. Note that such a, b, c exist, since…

A:

Q: U = kuzx for 0 0, u(0, t) = u(L, t) = 0, u(x, 0) = x(L – x)

A: Given that, ut=kuxx , 0&lt;x&lt;L, t&gt;0u0, t=uL,t=0ux, 0=xL-x This is  the heat conduction problem…

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: O Grven rref(A)=.] and A represents for mation T: R→R, Tlu)=Au. State all rectors in Show work and…

A:

Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

A:

Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…

A:

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)_1 a(x,y) a(u,v)

A:

Q: In Exercises 19–22, r(t) is the position of a particle in space at time t. Find the angle between…

A: Consider the first part: Consider the following position vector: rt=3t+1i^+3tj^+t2k^ Differentiate…

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

A:

Q: of at (x, y, z) = (2, 3, 4). ay Let f(x, y, z) = (x + y)z. Evaluate

A: Given :fx,y,z = x+yz

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). -=D1 a(x, y) a(u,v)

A:

Q: 3. Bir f (1,y, 2) = ee cos 5z fonksiyonu veriliyor. a) grad f (r, y, z) =? bulumuz. b) Bu…

A:

Q: Let F = (z, 2x, y) and C is the straight segment from (0,0,0) to (1,2,3). Then ,F dř = %3D %3D

A: Given,                                   F→(x, y, z)=z, 2x, yand C is the straight segment from (0,…

Q: 2. Wis subset of V- R3 where %3D a W={(x,y;-1) E IR³ | x, y eR}

A:

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: a2u 1 du 1 a?u = 0, ar? r dr (r,0) = 0, u(r,t)= 0, 0 <rsland u(1,0) = 0 pour 0ses %3D

A: Given,                  ∂2u∂r2+1r∂u∂r+1r2∂2u∂θ2=0                             (1)with u(r,0)=0,…

Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

A:

Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.

A: we have to partial derivative with respect to u by using chain rule

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

A:

Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: a Fmiel fhe Langth and directin ofuxv and vXu by Uz } i-tj+K , V= i+j+2K

A:

Q: 5={cj+ kn, u +vn): nez T={(x,y)EZ:157 x +107 y =- 157 x +107y=1 choose j,K, u,v EZ, such that S=T"…

A: Linear Diophantine equation: A linear Diophantine equation in two variables takes the form of…

Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: Consider Uu=4uzzy u(x,0) = u(x), u₁(x,0) = u₁(x), on the domain -∞<x<∞, 0≤t<∞o. Suppose that both…

A:

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

A:

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

A:

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

A:

Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

A:

Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

A:

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

A:

Q: Let's Apply u = {p, a, t, h, f, i,n, d, e,r} Given X = {p, a, n, t, h, e,r} Y = {f,a, t, h, e,r} Let…

A:

Q: 7 In the figure MN | OP and ZOST= 73°. %3D Find the measure of ZMTS and ZSTN. M T 73° R. P. A ZMTS…

A: We have to find the angel

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer