SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

Q: FIND THE GIVEN DIFFERENTI Homogeneous Eguation ( 3x + 4y) dx - dy -0

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (d) z = sin (4x + 5y); x = s + t, y = s - t

A: Given that, z=sin4x+5y ; x=s+t ; y=s-t Then we get, z=sin4s+t+5s-t⇒z=sin4s+4t+5s-5t⇒z=sin9s-t

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

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Q: Find a. Əw dx a. aw əx and b. y (2π,1,-π) Əw at the point (x,y,z) = (2π, 1₁ - π) if w = x² + y² + z²…

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: 3- show that the diff. equ. is homogeneous and Solve it (2x +34) dx + (y-x)dy = 0

A: To find the solution of the given differential equation(DE).

Q: ( b) SI[ vzcos(x* µV where E = {(x, y, z) |0 < x < 1, 0 s y s.x, x S z 5 2x } E

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Q: SSS 12z dV E where E is enclosed by z = x? + y² and z = 1 О Зл O 27 O 4T O JT

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Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: To integrate x3x² dx' Ox хех2 242 x² OX we apply integration by parts and in the form u dv, dv is…

A: We have to determine the integral

Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: i) ais f(x,y) = x2 + 3xy + y -1 Laalic * Te Te

A: Given that  Af(x,y)=x^2+3xy+y-1  To find the partial differentiation of f(x,y)

Q: The volume V of a right circular cylinder of radius r and height h is V = ar?h. (a) How is 4 related…

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Q: зхе-МХxcos(Nx) 5- a. Differentiate: y = M csc(Nx)+Nx

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Q: Find the most general antiderivative of f(x) = 7e" – 8 sec? (x), where ř < x < 5.

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Q: (b) Given that y, = z sin(ln z) solves r*y" – xy + 2y = 0, %3D

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

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Q: An integrating factor for y'+8z°y = sin z is given by (a) 2z (b) In(z*) (c) z4 (d) 5e2z

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Q: 3 13. If x = u + v³ and y = uv – v² are solved for u and v in terms of x and y, evaluate ди ди dv dv…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = ln (x + 2y + 3z)

A: Given, ƒ(x, y, z) = ln (x + 2y + 3z)

Q: sec z dr

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Q: fz? +z+1 I = dz co

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

Q: Solue d?3e 2 +4x=5in zt using methoel I Vorintion of parameters .

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Q: 26. y = sinh x, y= e, x = 0, x= 2 27. y = Vx, y =;x, x= 9 28. y =x, y = 2.x², x + y = 3, x>0 II

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: yit yä - 2xyzk b. V= xy Sin Z (i +2+ e)

A: Please check step 2 for the solution.!

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: T(z, Y, 2) = 1500e 2y

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Q: (b) [₁³ sin (π(x – 2y)²) dA, where T is the triangle bounded by x – 2y = 1, y = −3x and 5y = -x.

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Q: flx, v) = { xe-x(1 + y) x20 and y 2 0 otherwise rmine E(XY). ulate Cov(X, Y) and p. X, Y) =

A: Given Two components of a minicomputer have the following joint pdf for their useful lifetimes X and…

Q: 1. Evaluate a dV where E = {(x, y, 2) E R³ | 0 < z < x + y,0<x < y?,0 < y< 1}.

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Q: uct Theorem. 10. K y KM=

A: Solution

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation

Q: The volume V of a right circular cylinder of radius r and height h is V=πr2h (a) How is dV/dt…

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