xy If z show that: x- y

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: Show that if F = xi + yj + zk, then ∇ * F = 0.

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Q: z = If X – y show that: =D0

A: Given: z=xyx-y And x2∂2z∂x2-y2∂2z∂y2=0   As we know that; The Quotient rule; fg'=f'·g-g'·fg2 The…

Q: Let f(æ, y) axy + az?y+ y³. (a) div(grad(f)) = (b) Find a so that div(grad(f)) = 0 for all æ, y. %3|…

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Q: If f(x, y) = xsec²2y + ycosec²2x + 2xy then show that, drdy dydx

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Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

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Q: Find fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

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Q: Find the value of c such that S xe = 3.

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

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

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Q: y z = x + show that : 0.

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

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Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: Obtain characteristics y² Uxx + Uyy = O

A: Given equation is  y2Uxx+Uyy=0 Now comparing with  AUxx+BUxy+CUyy=0 We have A=y2, B=0, C=1

Q: dy let y = xtan z then is da elect

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Q: for z = In(2® + y*). Find

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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: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: If w = x*y+y*z+2x, Verify the following identity: dw dw dw + ax' dy' az = (x + y + 2)²

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Q: If S(x, y)= x² +y , find f, and f, . %3D Vr

A: Fx is partial differentiation of F with respect to x.

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

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Q: Need help on showing how to prove this      (x(y+z))w=(xy)w+x(zw)

A: Expressions are mathematical statements that have a minimum of two terms containing numbers or…

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

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Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: 3. Given z =, show that ху xy(zxx + Zyy) уз — х3 2 || x²y2

A: δwδt=δwδxδxδt+δwδyδyδt+δwδzδzδt       =ysin(z2).(-1)+xsin(z2).0+2xyzcos(z2)(2t)

Q: If Z = x.n. f (), then show that: x. Zx + y.Zy = z

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Q: b) Find if f(x, y) = ysin( xy)

A: Givenf(x,y)=ysin(xy)find ∂w∂t

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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

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Q: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: If z = x – 3y, then w = 2 Using the calculation above, mark the s

A: Linear span: Let V represent a vector space, and S=v1,v2,...,vn represent a subset of V. If every…

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

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Q: if y ". y (In z) (a) Find

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Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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

A: On doing partial differentiation we will get

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

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Q: a) If z= xy – xey/= , show that x * + y = xy+ z.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: let f(x, y, z) = 2x?y + 3xyz-x z+3y Find: fx . fxy, frz fryz

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Q: Evaluate G(x,y)dy , if Gx.y)=2xy ,x 5cost ,y 5sint ,0stsm/3.

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.