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.

Q: Evaluate the line integral. | (9x – 9y) ds C C : x² + y² = 64 | (9x – 9y) ds = C

A: Explanation of the solution is given below...

Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

A:

Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

A:

Q: if was T!R R? Linearidentifir grandfather OkerT ImiT

A:

Q: let (X; Z) v it piece wise comnected ?

A:

Q: If U = span {x, y, z} in Rn, then show that U = span {x + tz, y, z} for all values t∈R.

A:

Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Wnete to y=2x=1 equotion for Hhe line Pacallel the Doinit 4,9) an and

A:

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: Find ∂w/∂r for w = yz/x, x = θ2, y = r+θ, z= r-

A: To evaluate ∂w∂r

Q: Let f(r, y) = (3 – y)". Then %3D drdy drðydr

A:

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

A:

Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

A:

Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

A:

Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

A:

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

A: The given function.

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

A:

Q: If (x, y) > (x+3, y-7) maps TUVW to T'U'V'W', what is the algebraic description that will map…

A: x, y→x+3, y-7 maps TUVW to T'U'V'W'. That is, the x-coordinates of T, U, V and W are added by 3…

Q: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: , find the Jacobian ?(x, y)?(u, v) for the indicated change of variables x = uv − 2u, y = uv

A:

Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: (b) If z =W, show that: x- y xy 0 =

A:

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

A:

Q: a. In R?, let C be the line segment from (-1,2) to (0, 4), and let F = (x + 2,-xy). Evaluate S, F ·…

A:

Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

A:

Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

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

A: Change the z in the terms of u and v and the differentiate.

Q: a) If W =(x,y), where x v²-g' and y 2vg calculate W+ %3D

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: Let X= R, and defined d as d(x,y)= lyl then verify that if (1) d(x,y)=d(y,x) (2) d(x,y) =0 iff x =y…

A: Given : dx, y=y (1) So, dy, x=x≠y So, dx, y≠dy, x

Q: Let z = 3x*y, find Vz.

A:

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

A:

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. v), y = (u + v) X = -

A: The formula for the Jacobian is: ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v

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: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

A:

Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: Let w = 4x? + y? + z? x = psinpcose y= psinpstno z = pcoso Find dw dw dw de ee de

A:

Q: Be u = x2 + yz, where x = rsin(t), y = rcos(t) and z = rsin2(t), calculate: ∂u/∂r and ∂u/∂t

A:

Q: If z xy? +x°y, find zZxxy and Zyxy %3D

A: On doing partial differentiation we will get

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

A:

Q: Given f(x, y, z) = 4x2 + 2y? + 6z?, find %3D fa(x, y, z) = fy(x, y, z) = f:(x, y, z) =

A: To find fx(x,  y,  z) =........... fy(x,  y,  z) = ...........  fz(x,  y,  z) =............

Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

A:

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.