If u=2x+y and v=x-2y then the st ream line is y? x2 Pxy+ 2 2 ylgn ihi

Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

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Q: We know that S(x,y)dx + g(x,y)dy] = Se f(x,y)dx +Seg(x,y)dy. Use this knowledge to evaluate S.y dx+x…

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Q: Given y 16e4x + 5e find y. %3D A. y = 16e4x + 5e + c В. у %3D 16е4* + 5ех + с y = 4e4x + 5ex+c D. y…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x = 1+2t, y=5+15t, z=-2+6t,…

A: given : the equations of two skew lines are: L1: x=1+t, y=1+6t, z=2tL2: x=1+2t, y=5+15t, z=-2+6t D…

Q: 20. Evaluate l Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: E valuate f win Tydy tyxdx olE Cethe line seqment f&Om (0,2) to

A: on solving this we get the

Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: df If f(x,y,z) = In(x² – y²z+ yz³) then find Əz 3yz? + y? (x² - y²z + yz³) 3yz? - y? (x² – y²z +…

A: The equation is fx, y, z=lnx2-y2z+yz3.

Q: Given f(r, y) = yln(5z+ y), find .(e, v) - 1,(2, u) = %3D

A: We have to find derivative

Q: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given query is to find indicated partial derivative.

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: 2. Evaluate (x² + iy) dz, where C is the straight line from z = 1 to z = i.

A: to find  ∫Cx2+iy3dz,  where C is the straight line from z=1 to z=i proof using giving condition we…

Q: In ARST, mZR = 47°, m 2S = 3y - 7, and mT = 2(y + 10). Find the value of y. %3D %3D %3!

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Q: Q3: if it was A(x, y, z) = x?yi + y?zj + z?xk and Ø(x,y,z) = xy + yz + zx find (a) A. (VØ) (b) Ø…

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Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: Find (au/ay), at the point (u,v)=(√2,-2), if x=u² + v² and y= uv. du (Simplify your answer.) ay…

A: Given x=u2+v2,y=uv   u,v=2,-2

Q: 2. Let c be the line from 5 to 2 + 3i. Find i. S. zdz ii. S. ždz

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Q: 20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A: here we the formulae   the a plane have normal n→=<a,b,c> and passes through a point (x1 ,y1…

Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

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Q: v(e -Y cos x) • dr, where C is the line from (0,0) to (2x, kn 7)

A: The fundamental theorem of line integral, also known as gradient theorem states that suppose a curve…

Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: dw dw Find ду and ду at the point (w, x, y, z) = (9,3,1,1) if w = x²y? + yz- z³ and x2+y² +z² = 11.

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

Q: If D is the distance between the skew lines 4 x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z=-2+6t, then…

A: first we will  convert given parametric equations of lines, then we will find  a1,b1,a2,b2 after…

Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: Show that if w = f(u, v) satisfies the equation fuu + fov = 0 and Q3) (Chain Rule) a² – y? if u =…

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Q: We are given w = 2yln(y+2z)x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: 2 If V) 3 ли?h +- л , where h %3Dh() and r e R, then V'(1) is A. 2ærh -r'(1) + Tr² · h'(1) +27r² ·…

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Q: Find y dy ·S= using the substitution u +5=√√y+21 Vy+2 ²/(√√y+2-5) (5√√y+2+y+24) +C…

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Q: Find y dy ·S using the substitution u +5=√√y+2 y+2 © ²(√√y+2-5) (5√/y+2+y+24) + C…

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Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z= -2+6f,…

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Q: What is P-(y) if the given DE is xydx – (3y – x²)dy = 0? -2y 2y 2 y -2y-1

A: Given : Linear differential equation  Need re write in x form as follows dx/dy +P(y)x=Q(y)

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Ex: Find and . fie 28. u = rs? In t; r = x², s = 4y + 1, t = xy³ %3D

A: ∂u∂x and ∂u∂y

Q: If u=2x+y and v=x-2y then the st ream line is y? x2 2xy+ 2 %3D

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Q: Evaluate | (x + iy' ) dz, where C is the straight line from z =1 to z=i.

A: given, C is the straight line from z=1 to z=i claim- evaluate the integral ∫Cx2+iy3 dz

Q: dw dw (a) ду (b) dy at the point (w, x, y, z) = (4, 2, 1, -1) if w = xy² + yz – z³ - 23 and x² + y?…

A: The given equation is w=x2y2+yz-z3 and x2+y2+z2=6 To find ∂w∂yx and ∂w∂yz

Q: dw and at the point (w, x, y, z) = (22,1, – 1, – 2) if w =2x²y? +2yz- 2z° andx? +y² +z? = 6. Find…

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Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: We are given w = 2yln(y+2z)+x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of ryg is (a) 6 %3D…

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Q: a. The y' for y = (u – 4)z and u = x² + 4 b. The y' y = Vu and u = Vx

A: Given;          a.  y=u-432 and u=x2+4b.  y=u        and u=x a. Solve for y'…

Q: Use the given information to find Ax, Ay, and dy. 1 :x decreases from 2.5 to 2. х — 1 y = Ax = Ay =…

A: Given: y=1x-1; x decreases from 2.5 to 2

Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Ion 41 Let A = (m, n) and B = (x, y). If A and B lie in on horizontal line and B is to the right of…

A: We will solve the problem using figure.

Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ