Evaluate O xy?dx + x5dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: T(x, y, z) =? (a) (x + 2y, -y- 2z, -2) (r = y, 2x = 3y + z) (b) (c) (x – y, 2x – 3y – 2) (d) - - (x…

A: Given matrix is, A=1-102-3-1 The formula for finding the linear transformation is, Tv=AvT

Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

Q: Evaluate = (VIn(x°cos(#)) – 24) dr + (4r – 3°evtm(7*) dy (4.r – y°e2ytan(y") where C, is the…

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Q: Find the average value of f(x, y) over the plane region R.

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Q: E = {(x,y, z) E R³ |z² + y³ < z< 12 – 2x² – 2y²}. %3D

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Q: Which conclusion does the diagram support? W V Y O A. VW UV ZY YX В. VY UZ WX VY C. UZ = WX 2 D. VY…

A: It is known that when any two transversals, cut 3 or more than 3 lines, then they cut the…

Q: Which conclusion does the diagram support? W V Y U UV ZY А. VW YX VY UZ В. WX VY C. UZ WX O D. VY =…

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Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: Find r, y, z and t where 6. + 2t 4 r+y 3 %3D -1 2 +t

A: Given  3 xyzt = x6-12t + 4x+yz+t3 We have to find x, y, z and t.

Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

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Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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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: Young dribbles the ball according to the rule (x,y) -&gt; (x, y - 10) and then passes the ball…

A: Young dribbles the ball according to the rule (x,y) -&gt; (x, y - 10) and then passes the ball…

Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D 4.

A: We will find the dimension of W

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = x - √(y2 + z2)

A: Given function is, f(x,y,z)=x-y2+z2

Q: 1 Set up and evaluate , 6x dA, where R is the rectangular region with corners (-2, 0), (3,0), (-2,…

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Q: 1. f(x, y) = 192x³ + y² – 4xy2 on the triangle with vertices (0,0), (4,2) and – 2,2). %3D

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

Q: U + 2ru, =0 IER, t> 0, u(x,0) =e=.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D

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Q: Find the cross product a × b. a = (t, t2, t3),      b = (1, 6t, 8t^2)

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Q: -)using change of variables to evaluate: x+y 'R (2-x+y) (1,0),(0,1),(-1,0),and (0,–1) dædy ,where R…

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Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: Evaluate ſ √x² + y²dxdy over the triangle with corners (0,0), (4,4), and (4,0) using x = u, y = uv.

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Q: Find the Jacobian ",Y,2) where u = yz, v = z, w = x + g 8(u,v,w)

A: We have been given  u=yz,v=z,w=x+y First, we will convert the functions x, y, and z in terms of u,…

Q: Evaluate O xy°dx + x²dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

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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: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: Evaluate eリ+1 dA D where D is the triangle with vertices (0,0), (-1, 3), and (6, 2).

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Q: p ry*dx + x*dy, where C is the rectangle with vertices (0,0), (1,0), (1,5), and (0,5) Evaluate

A: We will convert this line integral to surface integral using greens theorem

Q: dw Find and using the chain rule. ди 3 w(x, y, z) = x = u² + v², y = u² + v², z = 2uv. %3D x² + y? +…

A: The solution is given as

Q: 3. Let x? + y² + z² = ? 3ryz, then which of the following is %3D 2y–3zy O a. 2z-3zy 3zy–2y O b.…

A: Note that, here x and y are independent variables and z is the dependent variable. So, we will apply…

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: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

Q: Exercises 41 and 42, evaluate (y – x) dx + (2x + 5y) dy. 41. C: line segments from (0, 0) to (2, –…

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Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: S. Re{z²}dz; C is the square with corners 0, 1,1+i, i. [1+i]

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Q: Evaluate o -dz where C :|z| = %3D (z-1) (z² – 5z +6) C

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Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

A: Recall:    If f(t) and g(t) are two function of 't' and h(t)=f(t)+g(t) then…

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

A: Connected and path connectedness

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: y = (c,+c,x)e¯*+ (c;+cx)e½ y = c,e*+c,e¬*+ (cz;+cx)e½ (4D4 - 4D3 - 3D2 - 2D + 1)y = 0. y =…

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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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: Find z and z, Zy. z = 2x*y5 !! %3D Zy %3D × | > N

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Q: (b) xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z < 0}.

A: We have to evaluate given integral:

Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

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Q: Find r'(t), r"(t), and r'(t) r(t) = (t2 + 9t)i – 3t2j %3D -

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