2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

Q: Find y' at the point (7, 7) where z sin(z? – y*) + 46 = z² – 3. Türkçe: z sin(z² – y²) + 46 = z² – 3…

A: To find y' at (7, 7) Where  x*sin(x2 - y2) + 46 = x2 - 3....(1)

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: L'équation 423 = In (e4% + 2ay) définit implicitement z comme fonction de x et de y au voisinage du…

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Q: 28. Evaluate by Green's theorem (x - cosh y) dx + (y + sinx) dy, where C is the rectangle with…

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Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

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Q: Can i get help step by step please

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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: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: If y=xtan(x) then dy at x = Tt is: dx

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Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: .3 Suppose that w = x³yz + xy + z + 3 and x = 3 cos t ,y = 3 sin t , dw z = 2t. Evaluate dt t= ドIN

A: Ans:  we will use product rule of differentiation to solve this question.

Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: e solution of the differen uation dy/dt 3 y with in ndition y(0) = 5 is %3D t

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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: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D

A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: Given w = In(") + 8z*y* /z find %3D mmadı zerinden mmis xy + 12.x ayu Ob. 72x y 12E +96x'y Od.…

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Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: Since z = In (x2 + y2), x = eucosv, y = eusinv əz/ðu =? az/dv =?

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Q: (3) +. R Ris bounded by the semicircle y = V2x – x² and the line y = x

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Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: dy sin(x + y) dx

A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…

Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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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: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:…

Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

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Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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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: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.