Q5: ди ди ди and dz p-q a. Find for u = if p = x + y + z ,and q = x + y + əx' əy q-r z, and r = x+ y – z, at the point (x, y, z) = (V3,2,1). %3D

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: 4. Let w = f (z) = 2iz + 67, find u and y and the value of f at z =+ 4i %3D %3D Z ==+

A: We need to find u, v and value of f at z.

Q: prs is Linearly independent. please prove it. z set A is orthogonal if Por every Xy>X_eA, we have 2.

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)

A: Solution :

Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

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Q: dw dw and du For the functions w =xy + yz + xz, x=u + v, y =u - v, and z= uv, express using the…

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Q: Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

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Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Let f(x,y) = x² – xy+y² – x. Find the direction u and the value of Duf(1, – 1) for which Duf(1, – 1)…

A: We have to find maximum directional derivative.

Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

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…

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Q: = a + zy", z - w* + w, y I = uu" + w", y u+ ve fi az Find when u = 1, v 2. w=0 = %3D H.

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Q: Find the Jacobian for the indicated change of variables. x = uy -2u, y = uv О д(x,y) H(u, v) О…

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Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: Q2 Let C be the line segment joining the origin and the point (2,0, 1) and C2 be the line segment…

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Q: a) Lollowng use Euler ncthoel tsoule The d = yx2-Y for メ=2 at h=o.Ś , h=0.25 y= x +zy h=ol y (2)= }

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Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: nto v. t of u orthogonal to v.

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Find Vf at the given point. f(x,y,z) = x3 + y2 – 3z2 +z In x, (1,2,4) Vil(1,2,4) =Di+j + ()k ( %3D

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Q: u'+ y enx =0 differantial equartion find the %3D pardiculbr general soution. and

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Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: Use the transformation u = - -6x +y, to evaluate the integral [ ( (5x • y) dx dy, where R is the…

A: use the transform u=-6x+y, v=5x+ywe evaluate ∫∫R 5x+y dx dywhere R is the parallelogram bounded by…

Q: Compute fS fdS for f(z,v, z) = 2y-z and S is the part of the cone 2-2+ betweenm z 1 and z 4.

A: Integration is the process of finding the anti-derivative function of a given function. The…

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: Evaluate S S12zdV E where E is the solid enclosed by z = 1 and z = x² + y² 2. Immmmm

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Q: 4) Verify that Green's theorem is true for f,xy?dx – x²ydy ,where C consists of y = x² from (-1,1)…

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Q: Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2,…

A: To determine the first order (linear ) approximation to f(x,y) at the given point

Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: 2) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…

A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u  and…

Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: 1+iz if w= Find the image |z|<1 1-iz

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Q: d) Find for w = xy + yz + xz , x = u + v , y = u – v , z = uv dv %3D at the point (u, v) = (-2,3).…

A: Given, The  functions  W=xy + yz + xzx=u+v,y=u-v,z=uv and the point is (u, v) = (-2, 3).

Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 52?yk. 3: 62. div F= curl F=

A: A detailed solution is given below

Q: J f ds if Evaluate Of(x, y, z)=x+y, and C is the combinations of lines connecting adjacently the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) &lt; ( 0, 0 )…

Q: F(x, y, z) = xyzi+ (2ry+2) j+y°z°k conservative?

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Q: Let f(x,y) = x² + xy- y² – x. - x. Find the direction u and the value of Duf(1,1) for which Duf(1,1)…

A: According to question we need to find for (x,y) = (1,1) So, I am assuming there is a typo in options…

Q: D.Prove that y y(2)= U12,9)+ jve (2,4) anelyli the loplale's as z, than Guetion u and v Satiglics

A: Consider an analytic function f(z) of the form . Then f(z) will satisfy the Cauchy-Reimann equation…

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Integrate f(x,y,z) = x + √√y-z² over the path from (0,0,0) to (4,16,4) given by C₁: r(t) = ti+t²j,…

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Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…