1) Calculat e S hCxiy)ds given that -(xiy)=xyi+y?g and Cis given by ?(t)=titt?g t€£0,1].

Q: If C is given by x = 1, y = 1, where 0 sts 1, then xy ds = 12 dt.

A: We have to check the value of the given integrals. If C is given by x=t, y=t where t is from 0 to 1.…

Q: If we use IBP to evaluate Ixe xe²x dx, then the most suitable choice for u and dv are

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Q: d'u = (1+3xyz+x*y°=²)e² dxdydz xyz If u = e-,show that 1+ 3xyz + x y:

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Q: If z = æe", then dz = (ev)dx + (aye) dy. Select one: OTrue OFalse

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

Q: If x"y" = (x+y)* m, m+n d'y prove that = 0 .2 dx?

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: 16. If m/STU = (13x – 6)', mSƯ = (21x + 8)', and mUT = 143', find mST. %3D %3D U T

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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: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If W = 2x3 + 3y², a 5t2, y = 2t³ %3D = %3D dW then find at t= 1 dt O 1912 O None O 1273 O 1572 2212

A: A detailed solution is given below

Q: IF. dr where C is the line segment from ( C (yz) + 1)i + (xz cos(yz) + 2y)j + (xY cos

A: The answer is 88

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: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: If e dy then y-

A: We will evaluate the following Integral.

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: 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: If A = 2x î + 3yĵ – z k and x = t² , y = t and z = t + 2; then the value of ſc À · d¯ from t = 0 to…

A: A = ( 2x, 3y, -z ) and C : ( x, y, z ) = ( t2, t , t + 2 ) for t = 0 to t = 1. We have to evaluate…

Q: Show that fdx + gdy = S 36x°y?dx + 18yx*dy is independent of path: (3,6) (-2,4) (3,6) 2,4) C(3,6)…

A: The vector field is conservative if the components satisfy the test ∂P∂x=∂Q∂x. If the field is…

Q: If y = t“, then dy 4t³. dt

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Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

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

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Q: If W = xy ++1 azw Show that дхду ey a2w %3D дудх

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Q: (a) Compute S ædx + ydy + (x + y – 1)dz where C'is the line segment from (1, 1, 1) to (2, 3, 4).

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Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

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Q: Given the following table : Ex = 84 E(X,-x)(y,-y)=-64 %3D Ey= 37 Σ-3 385 %3D n = 20 E(y,-y) = 1900…

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Q: In x - direction (+ -) - Fu + P,A,- P3A3 cos 40° m, V, cos 40° - m, V. F = P1A,- P3A, cos 40° + m,…

A: To identify for True or False.

Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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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: T (x, y) (2x,y) is an is %3D

A: T(x,y)=(2x,12y) The transformation of any figure changes the size, shape and the position to create…

Q: a?u du k 00 at Subject to the condition u(0, t) = 0, u(L, t) = 0 50x u(x,0) = f(x) = 50 – L. 0<x<L

A: Please check step 2 and 3 for solution

Q: Compute, [(1 – ye-")dx +e¯*dy where C is any path from (0, 1) to (1, 2).

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Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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

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Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: O, x = 2, y = dy dz is

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Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: Solve the initiol volwe problem using Laploce tronsformotion, y - e"sint y (4) + 2y' (+) +5y(+) y…

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: dv E={my,)|→<y<4Y<そく4, Osns? そ

A: Given that  Triple integral of z/(x^2+z^2) To evaluate the integral

Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…